
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 right triangle has perimeter  $2008$ , and the area of a circle inscribed in the triangle is  $100\pi^3$ .  Let  $A$  be the area of the triangle.  Compute  $\lfloor A\rfloor$ .

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