
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
Find the area of circle $\omega$ where points $P=(7,15)$ and $Q=(11,9)$ lie on $\omega$. Suppose that the tangent lines to $\omega$ at $P$ and $Q$ intersect at a point on the x-axis. Determine the area of $\omega$.
A) $709\pi$
B) $700\pi$
C) $650\pi$
D) $475\pi$

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