
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 $O$, diameters $\overline{AB}$ and $\overline{CD}$ are perpendicular to each other. A chord $\overline{DF}$ intersects $\overline{CD}$ at $E$. If $DE = 4$ and $EF = 4$, calculate the area of the circle.
A) $16 \pi$ 
B) $24 \pi$ 
C) $30 \pi$ 
D) $32 \pi$ 
E) $36 \pi$

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