
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Proof of the Pythagorean theorem based on cutting and rearranging shapes. Squares are constructed on the sides of an arbitrary triangle. Cut the squares constructed on the legs (the two shorter sides) into pieces so that these pieces can be rearranged to form the square constructed on the hypotenuse (the longest side).

Present the answer in LaTex format: \boxed{Your answer}
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