
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 the diagram, \( \overline{AB} \) and \( \overline{CD} \) are diameters of a circle with center \( O \), and \( \overline{AB} \) is perpendicular to \( \overline{CD} \). Chord \( \overline{DG} \) intersects \( \overline{AB} \) at point \( F \). If the lengths of \( DF \) and \( FG \) are 8 and 4 respectively, find the area of the circle.
A) \( 25\pi \)
B) \( 30\pi \)
C) \( 32\pi \)
D) \( 35\pi \)
E) \( 40\pi \)

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