
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 circle is inscribed in a right triangle $PQR$ where $\angle PQR = 90^\circ$. The circle is tangent to $PQ$ at point $M$ and to $QR$ at $N$, and the points diametrically opposite $M$ and $N$ lie along the hypotenuse $PR$. Given that $PQ = 9$ and $PR = 15$, calculate the area of the portion of the circle that lies outside the triangle $PQR$.

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