
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 $P = (3, 7)$ and $Q = (7, 5)$ lie on a circle $\Omega$. It's known that the tangent lines to $\Omega$ at $P$ and $Q$ intersect at a point on the $x$-axis. Determine the area of $\Omega$.

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