
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
Triangle ABC is a right triangle with AB as the hypotenuse. Let O be the center of its inscribed circle, and the length of AC is twice that of BC. If the area of the circle is $4\pi$ sq cm, what is the area, in square centimeters, of triangle ABC? Express your answer in simplest radical form.

Note: The area of a circle with radius $r$ is $\pi r^2.$

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