
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 \(ABC\) has a perimeter of 54, with the leg \(AC\) being greater than 10. A circle with a radius of 6, whose center lies on leg \(BC\), is tangent to lines \(AB\) and \(AC\). Find the area of triangle \(ABC\).

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