
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
Two points, $A=(7,14)$ and $B=(13,12)$, are on a circle $\omega$. The tangent lines to $\omega$ at $A$ and $B$ intersect at a point on the $x$-axis. Find the area of $\omega$.
A) $176\pi/5$
B) $176\pi/3$
C) $196\pi/1$
D) $196\pi/3$
E) $196\pi/5$

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