
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
An equilateral triangle $DEF$ has side length $6\sqrt{2}$. A circle with radius $4\sqrt{3}$ is tangent to side $DE$ at point $D$ and to side $DF$ at point $F$. Calculate the area of the circumcircle of triangle $DEF$.
A) $18\pi$
B) $24\pi$
C) $36\pi$
D) $48\pi$

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