
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
In triangle XYZ, angle XYZ is a right angle. The three quadrilaterals shown are squares on each side of the triangle. The sum of the areas of the three squares is 450 square centimeters. Find 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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