
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 concentric circles share the same center, denoted as $C$. A chord $\overline{AD}$ of the outer circle is tangent to the inner circle at point $B$. The radius of the outer circle $AC$ is $12$ units, and the length of the chord $\overline{AD}$ is $20$ units. Find the area between the two circles.
A) $81\pi$
B) $100\pi$
C) $120\pi$
D) $144\pi$

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