
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 Z is a right angle. Four squares are constructed such that each square has one side aligned with one side of the triangle or with the hypotenuse. The sum of the areas of these four squares is 722 square centimeters. Determine the number of square centimeters in the area of the largest square.

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