
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 an isosceles right triangle, a square is inscribed such that one of its vertices touches the hypotenuse, and its two adjacent sides lie along the two legs of the triangle. If the area of this square is $484 \text{ cm}^2$, what is the area of a square inscribed such that it shares a part of one leg and the hypotenuse with the triangle?

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