
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 XYZ is a right angle. There are three quadrilaterals, all squares, connected to this triangle. The sum of the areas of these three squares is 450 square centimeters. Determine the area of the largest square.

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