
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
Points \( P = (2, 9) \) and \( Q = (8, 7) \) are on a circle \( \Omega \) in the plane. The tangent lines to \( \Omega \) at \( P \) and \( Q \) intersect at a point on the x-axis. Determine the area of circle \( \Omega \).
A) \( \frac{243\pi}{9} \)
B) \( \frac{365\pi}{9} \)
C) \( \frac{730\pi}{18} \)
D) \( \frac{730\pi}{9} \)

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