
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
Angle ABC is a right angle. The diagram shows four quadrilaterals, where three are squares on each side of triangle ABC, and one square is on the hypotenuse. The sum of the areas of all four squares is 500 square centimeters. What is the number of square centimeters in the area of the largest square?

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