
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 isosceles triangle $DEF$ has $DE = DF = 5\sqrt{3}$, and a circle with radius $3\sqrt{3}$ is tangent to line $DE$ at $E$ and to line $DF$ at $F$. What is the area of the circle that passes through vertices $D$, $E$, and $F$?
A) $63\pi$
B) $48\pi$
C) $72\pi$
D) $36\pi$
E) $54\pi$

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