
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
In a circle with center $O$, $\overline{AB}$ and $\overline{CD}$ are diameters perpendicular to each other. Chord $\overline{DF}$ intersects $\overline{AB}$ at $E$. Given that $DE = 8$ and $EF = 4$, determine the area of the circle.
A) $24\pi$
B) $30\pi$
C) $32\pi$
D) $36\pi$
E) $40\pi$

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