
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 two of its vertices are on one leg and one vertex on each of the hypotenuse and the other leg. If the area of this square is found to be $625 \text{cm}^2$, find the area of another square inscribed in the same triangle with one vertex each on the hypotenuse and one leg, and two vertices on the other leg. [Optionally, include a diagram similar to the original for clarity.]

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