
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
Points \( D, E, F \) lie on circle \( O \) such that the line tangent to \( O \) at \( D \) intersects ray \( \overrightarrow{EF} \) at \( P \). Given that \( PD = 4 \), \( PF = 2 \), and \( \angle FPD = 60^\circ \), determine the area of circle \( O \).

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