
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 $\angle ABC = 90^\circ$. A circle is tangent to sides $AB$ and $BC$ at points $X$ and $Y$ respectively, such that the points on the circle diametrically opposite $X$ and $Y$ both lie on side $AC$. Given that $AB = 9$, find the area of the portion of the circle that lies outside the triangle.

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