
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 points $P=(4,11)$ and $Q=(10,9)$ be on circle $\tau$ in the plane. Suppose that the tangent lines to $\tau$ at $P$ and $Q$ intersect at a point on the $x$-axis. Find the area of $\tau$.
A) $\frac{99\pi}{10}$
B) $\frac{101\pi}{10}$
C) $\frac{107\pi}{10}$
D) $\frac{109\pi}{10}$

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