
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 $ABCD$ be a square with side length 10. A circle is inscribed such that it is tangent to two adjacent sides, $AB$ and $AD$, with tangent points $X$ and $Y$ respectively. The point on the circle diametrically opposite $X$ lies on the side $CD$. Find the area of the portion of the circle that lies outside the square.

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