
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
A triangle has side lengths of 15, 36, and 39 units. Verify if it is a right triangle. If it is, consider a square inscribed in the semicircle where the diameter is the hypotenuse of this right triangle. Calculate the area of the square.
A) $759$
B) $760.5$
C) $1521$
D) $1520.5$

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