
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
Consider a right triangle ABC (where angle BAC is 90°) with lengths of \(AB = 63\text{ cm}\) and \(AC = 16\text{ cm}\). A square is inscribed such that one of its sides lies along \(BC\) (the hypotenuse). What is the area (in \(\text{cm}^2\)) of a square inscribed in this triangle with a vertex touching \(A\) and the opposite side parallel to \(BC\)?

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