
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
Let \( ABC \) be a right triangle with \( \angle BAC = 90^\circ \) and \( AB = 9 \). A circle is tangent to the sides \( AB \) and \( AC \) such that the points diametrically opposite the points of tangency both lie on \( BC \). Calculate the area of the portion of the circle that lies outside the triangle.

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