| Tasks | 6 |
| Train | 1 (16.7%) |
| Test | 1 (16.7%) |
| Duration | - |
| Avg | - |
| Errors | 0 |
| Description | - |
| Tokens | 259,435 |
| In Tokens | 209,164 |
| Out Tokens | 50,271 |
| Retries | 0 |
Session Configuration & System Prompts (7 files)
coder_system_context.md
# SYSTEM System is SEER, an agent in training to develop skills for solving tasks by determining the transformation rule from sets of example input and output data. ## Key Objectives - **Develop perceptual capabilities**: + Recognize objects, relationships, and patterns in the data. - **Discern transformation logic**: + Formulate precise natural language programs describing how inputs transform to outputs. - **Iterative learning and validation**: + Use examples, code execution, and validation strategies to refine hypotheses and outputs. Our goal is to achieve a deep understanding of perceptual and procedural reasoning to construct accurate solutions for unknown tasks. This involves interpreting input-output data and synthesizing natural language programs that describe transformation rules. Our mission is to understand and improve your perceptual capabilities and your ability to discern patterns. A key skill that we want you to develop is your ability to describe the context of each task and how to develop the solution. We will call this a natural language program. At this stage, we are most interested in your ability to determine the "story" of each task - a description of how the input data is transformed to the output data as a general rule, expressed as a natural language program.
config.json
{
"output_dir": "./sessions",
"roles": {
"dreamer": {
"model_name": "gemini-2.0-pro-exp-02-05",
"generation_config": {
"temperature": 1.0,
"top_p": 0.95,
"top_k": 64,
"max_output_tokens": 8192,
"response_mime_type": "text/plain"
},
"system_context_file": "config/system_dreamer.md"
},
"coder": {
"model_name": "gemini-2.0-pro-exp-02-05",
"generation_config": {
"temperature": 1.0,
"top_p": 0.95,
"top_k": 64,
"max_output_tokens": 8192,
"response_mime_type": "text/plain"
},
"system_context_file": "config/system_coder.md"
},
"oracle": {
"model_name": "gemini-2.0-pro-exp-02-05",
"generation_config": {
"temperature": 1.0,
"top_p": 0.95,
"top_k": 64,
"max_output_tokens": 8192,
"response_mime_type": "text/plain"
},
"system_context_file": "config/system_oracle.md"
}
},
"task_context_file": "config/task_context.md",
"investigate_nlp": "config/investigate_nlp.md",
"investigate_code": "config/investigate_code.md",
"max_iterations": 5
}dreamer_system_context.md
# SYSTEM System is SEER, an agent in training to develop skills for solving tasks by determining the transformation rule from sets of example input and output data. ## Key Objectives - **Develop perceptual capabilities**: + Recognize objects, relationships, and patterns in the data. - **Discern transformation logic**: + Formulate precise natural language programs describing how inputs transform to outputs. - **Iterative learning and validation**: + Use examples, code execution, and validation strategies to refine hypotheses and outputs. Our goal is to achieve a deep understanding of perceptual and procedural reasoning to construct accurate solutions for unknown tasks. This involves interpreting input-output data and synthesizing natural language programs that describe transformation rules. Our mission is to understand and improve your perceptual capabilities and your ability to discern patterns. A key skill that we want you to develop is your ability to describe the context of each task and how to develop the solution. We will call this a natural language program. At this stage, we are most interested in your ability to determine the "story" of each task - a description of how the input data is transformed to the output data as a general rule, expressed as a natural language program.
oracle_system_context.md
# Oracle System Context
You are the Oracle, a verifier and code analyzer for the ARC (Abstraction and Reasoning Corpus) challenge. Your role is to:
1. **Receive and Execute Code:** You will be given Python code designed to solve an ARC task. This code will define a `transform` function that takes an input grid (a list of lists of integers) and returns an output grid.
2. **Test the Code:** You will execute the provided code against the training examples of the ARC task. This includes:
* Running the `transform` function with the input grid.
* Comparing the transformed output with the expected output grid.
* Handling any errors (syntax errors, runtime exceptions).
* Capturing any print statements (standard output) from the code.
3. **Analyze Results:** You will analyze the test results, identifying:
* Successful transformations (where the output matches the expected output).
* Failed transformations (where the output does not match).
* Specific errors encountered during execution.
4. **Provide Feedback:** You will generate a concise summary of the test results, highlighting successes, failures, and errors.
5. **Generate Next Prompt:** Based on your analysis, you will create a new prompt to guide the Coder in fixing the code. This prompt should include:
* A summary of the analysis.
* The previous prompt that generated the code.
* Clear instructions for improvement.
You are a crucial part of an iterative process, helping the Coder converge on a correct solution. Your feedback should be precise and actionable. You do not generate code yourself; you guide the code generation process.session_summary_report.json
{
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"color_palette_correct": true,
"correct_pixel_counts": false,
"pixels_off": 4
},
{
"example": 2,
"input": "0 0 0 8 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 2 0 0\n0 0 1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0\n0 2 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0",
"expected_output": "0 0 0 8 0 0 0 0 0\n0 0 0 0 0 4 0 4 0\n0 0 7 0 0 0 2 0 0\n0 7 1 7 0 4 0 4 0\n0 0 7 0 0 0 0 0 0\n0 0 0 0 0 0 7 0 0\n4 0 4 0 0 7 1 7 0\n0 2 0 0 0 0 7 0 0\n4 0 4 0 0 0 0 0 0",
"transformed_output": "0 0 0 8 0 0 0 0 0\n0 0 0 0 0 4 0 4 0\n0 7 7 7 0 0 2 0 0\n0 7 1 7 0 4 0 4 0\n0 7 7 7 0 0 0 0 0\n0 0 0 0 0 7 7 7 0\n4 0 4 0 0 7 1 7 0\n0 2 0 0 0 7 7 7 0\n4 0 4 0 0 0 0 0 0",
"match": false,
"size_correct": true,
"color_palette_correct": true,
"correct_pixel_counts": false,
"pixels_off": 8
},
{
"example": 3,
"input": "0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 6 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 1 0 0 0 0 0\n0 0 0 0 0 0 0 0 0",
"expected_output": "0 0 0 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 6 0 0\n0 0 0 7 0 0 0 0 0\n0 0 7 1 7 0 0 0 0\n0 0 0 7 0 0 0 0 0",
"transformed_output": "0 0 0 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 6 0 0\n0 0 7 7 7 0 0 0 0\n0 0 7 1 7 0 0 0 0\n0 0 7 7 7 0 0 0 0",
"match": false,
"size_correct": true,
"color_palette_correct": true,
"correct_pixel_counts": false,
"pixels_off": 4
}
],
"006": [
{
"example": 1,
"input": "0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0",
"expected_output": "0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 0 0 0 0 7 0 0\n0 0 0 0 0 7 1 7 0\n0 0 0 0 0 0 7 0 0\n0 0 0 0 0 0 0 0 0",
"transformed_output": "0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 0 0 0 7 7 7 0\n0 0 0 0 0 7 1 7 0\n0 0 0 0 0 7 7 7 0\n0 0 0 0 0 0 0 0 0",
"match": false,
"size_correct": true,
"color_palette_correct": true,
"correct_pixel_counts": false,
"pixels_off": 4
},
{
"example": 2,
"input": "0 0 0 8 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 2 0 0\n0 0 1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0\n0 2 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0",
"expected_output": "0 0 0 8 0 0 0 0 0\n0 0 0 0 0 4 0 4 0\n0 0 7 0 0 0 2 0 0\n0 7 1 7 0 4 0 4 0\n0 0 7 0 0 0 0 0 0\n0 0 0 0 0 0 7 0 0\n4 0 4 0 0 7 1 7 0\n0 2 0 0 0 0 7 0 0\n4 0 4 0 0 0 0 0 0",
"transformed_output": "0 0 0 8 0 0 0 0 0\n0 0 0 0 0 4 0 4 0\n0 7 7 7 0 0 2 0 0\n0 7 1 7 0 4 0 4 0\n0 7 7 7 0 0 0 0 0\n0 0 0 0 0 7 7 7 0\n4 0 4 0 0 7 1 7 0\n0 2 0 0 0 7 7 7 0\n4 0 4 0 0 0 0 0 0",
"match": false,
"size_correct": true,
"color_palette_correct": true,
"correct_pixel_counts": false,
"pixels_off": 8
},
{
"example": 3,
"input": "0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 6 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 1 0 0 0 0 0\n0 0 0 0 0 0 0 0 0",
"expected_output": "0 0 0 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 6 0 0\n0 0 0 7 0 0 0 0 0\n0 0 7 1 7 0 0 0 0\n0 0 0 7 0 0 0 0 0",
"transformed_output": "0 0 0 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 7 7 7 0 0 0 0\n0 0 7 1 7 0 0 0 0\n0 0 7 7 7 0 0 0 0",
"match": false,
"size_correct": true,
"color_palette_correct": true,
"correct_pixel_counts": false,
"pixels_off": 5
}
],
"007": [
{
"example": 1,
"input": "0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0",
"expected_output": "0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 0 0 0 0 7 0 0\n0 0 0 0 0 7 1 7 0\n0 0 0 0 0 0 7 0 0\n0 0 0 0 0 0 0 0 0",
"transformed_output": "0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 0 0 0 7 7 7 0\n0 0 0 0 0 7 1 7 0\n0 0 0 0 0 7 7 7 0\n0 0 0 0 0 0 0 0 0",
"match": false,
"size_correct": true,
"color_palette_correct": true,
"correct_pixel_counts": false,
"pixels_off": 4
},
{
"example": 2,
"input": "0 0 0 8 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 2 0 0\n0 0 1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0\n0 2 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0",
"expected_output": "0 0 0 8 0 0 0 0 0\n0 0 0 0 0 4 0 4 0\n0 0 7 0 0 0 2 0 0\n0 7 1 7 0 4 0 4 0\n0 0 7 0 0 0 0 0 0\n0 0 0 0 0 0 7 0 0\n4 0 4 0 0 7 1 7 0\n0 2 0 0 0 0 7 0 0\n4 0 4 0 0 0 0 0 0",
"transformed_output": "0 0 0 8 0 0 0 0 0\n0 0 0 0 0 4 0 4 0\n0 7 7 7 0 0 2 0 0\n0 7 1 7 0 4 0 4 0\n0 7 7 7 0 0 0 0 0\n0 0 0 0 0 7 7 7 0\n4 0 4 0 0 7 1 7 0\n0 2 0 0 0 7 7 7 0\n4 0 4 0 0 0 0 0 0",
"match": false,
"size_correct": true,
"color_palette_correct": true,
"correct_pixel_counts": false,
"pixels_off": 8
},
{
"example": 3,
"input": "0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 6 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 1 0 0 0 0 0\n0 0 0 0 0 0 0 0 0",
"expected_output": "0 0 0 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 6 0 0\n0 0 0 7 0 0 0 0 0\n0 0 7 1 7 0 0 0 0\n0 0 0 7 0 0 0 0 0",
"transformed_output": "0 0 0 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 6 0 0\n0 0 7 7 7 0 0 0 0\n0 0 7 1 7 0 0 0 0\n0 0 7 7 7 0 0 0 0",
"match": false,
"size_correct": true,
"color_palette_correct": true,
"correct_pixel_counts": false,
"pixels_off": 4
}
],
"008": [
{
"example": 1,
"input": "0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0",
"expected_output": "0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 0 0 0 0 7 0 0\n0 0 0 0 0 7 1 7 0\n0 0 0 0 0 0 7 0 0\n0 0 0 0 0 0 0 0 0",
"transformed_output": "0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 0 0 0 7 7 7 0\n0 0 0 0 0 7 1 7 0\n0 0 0 0 0 7 7 7 0\n0 0 0 0 0 0 0 0 0",
"match": false,
"size_correct": true,
"color_palette_correct": true,
"correct_pixel_counts": false,
"pixels_off": 4
},
{
"example": 2,
"input": "0 0 0 8 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 2 0 0\n0 0 1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0\n0 2 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0",
"expected_output": "0 0 0 8 0 0 0 0 0\n0 0 0 0 0 4 0 4 0\n0 0 7 0 0 0 2 0 0\n0 7 1 7 0 4 0 4 0\n0 0 7 0 0 0 0 0 0\n0 0 0 0 0 0 7 0 0\n4 0 4 0 0 7 1 7 0\n0 2 0 0 0 0 7 0 0\n4 0 4 0 0 0 0 0 0",
"transformed_output": "0 0 0 8 0 0 0 0 0\n0 0 0 0 0 4 0 4 0\n0 7 7 7 0 0 2 0 0\n0 7 1 7 0 4 0 4 0\n0 7 7 7 0 0 0 0 0\n0 0 0 0 0 7 7 7 0\n4 0 4 0 0 7 1 7 0\n0 2 0 0 0 7 7 7 0\n4 0 4 0 0 0 0 0 0",
"match": false,
"size_correct": true,
"color_palette_correct": true,
"correct_pixel_counts": false,
"pixels_off": 8
},
{
"example": 3,
"input": "0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 6 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 1 0 0 0 0 0\n0 0 0 0 0 0 0 0 0",
"expected_output": "0 0 0 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 6 0 0\n0 0 0 7 0 0 0 0 0\n0 0 7 1 7 0 0 0 0\n0 0 0 7 0 0 0 0 0",
"transformed_output": "0 0 0 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 4 0 4 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 6 0 0\n0 0 7 7 7 0 0 0 0\n0 0 7 1 7 0 0 0 0\n0 0 7 7 7 0 0 0 0",
"match": false,
"size_correct": true,
"color_palette_correct": true,
"correct_pixel_counts": false,
"pixels_off": 4
}
],
"009": [
{
"example": 1,
"input": "0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 2 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0",
"expected_output": "0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 4 0 4 0 0
... [truncated for display] ...session_summary_report.md
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ Session Summary ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
Session Summary
┏━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━┳━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┓
┃ task ┃ prompt ┃ candidate ┃ total ┃ cached ┃ time (s) ┃ Test Score ┃
┡━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━╇━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━┩
│ 1-3aa6fb7a │ 21491 │ 6785 │ 28276 │ 0 │ 69.3090 │ 0/2 │
│ 2-0ca9ddb6 │ 44041 │ 10457 │ 54498 │ 0 │ 125.1168 │ 0/3 │
│ 3-1e0a9b12 │ 30013 │ 6619 │ 36632 │ 0 │ 130.3829 │ 0/3 │
│ 4-0d3d703e │ 38440 │ 8137 │ 46577 │ 0 │ 152.7588 │ 4/4 │
│ 5-150deff5 │ 41615 │ 8847 │ 50462 │ 0 │ 107.9591 │ 0/3 │
│ 6-0520fde7 │ 33564 │ 9426 │ 42990 │ 0 │ 118.9378 │ 1/3 │
└────────────┴────────┴───────────┴───────┴────────┴──────────┴────────────┘
task_context.md
# TASK CONTEXT
Your goal is to analyze and transform grid-based puzzles from ARC-AGI. Each task provides example input and output grids. The grids are 2D arrays (sizes ranging from 1×1 to 30×30) where each cell holds an integer (0–9) representing a color. Use the following color mapping:
```
0: white (238,238,238)
1: blue (30,147,255)
2: red (220,50,40)
3: green (79,204,48)
4: yellow (230,200,0)
5: gray (85,85,85)
6: magenta (229,58,163)
7: orange (230,120,20)
8: azure (135,216,241)
9: maroon (146,18,49)
```
**Task Overview**
- **Observation and Documentation:**
+ Examine the input and output grids.
+ Identify objects (contiguous blocks of
the same color), count color occurrences, and note geometric properties
(size, shape, position).
+ Summarize your findings in a YAML block.
- **Determining the Transformation Rule:**
+ Describe in natural language the step-by-step transformation observed.
+ objects, predicates and actions
- **Python Implementation:**
+ Using your natural language description, develop a Python function that
transforms any given input grid into the correct output grid.
+ Leverage common libraries (e.g., numpy, sympy) if needed, and ensure your
code covers all edge cases as per the transformation rule.
**Key Concepts and Priors**
- **Objectness:**
+ Objects are contiguous regions or patterns of the same color.
+ Objects persist and cannot appear or disappear without reason. Objects can interact or not depending on the circumstances.
- **Goal-Directedness:**
+ Some objects may have specific roles or “intentions.”
Objects can be animate or inanimate. Some objects are "agents" - they have intentions and they pursue goals.
- **Numbers and Counting:**
+ Use basic arithmetic and spatial reasoning to analyze objects’ size, shape,
and position.
+ Objects can be counted or sorted by their shape, appearance, or movement using basic mathematics like addition, subtraction, and comparison.
- **Basic Geometry and Topology:**
+ Consider both side-by-side and diagonal relationships.
+ Objects can be shapes like rectangles, triangles, and circles which can be mirrored, rotated, translated, deformed, combined, repeated, etc. Differences in distances can be detected.
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