
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
Given circle $O$, points $E$ and $F$ are located such that $E$ and $F$ are on opposite sides of the diameter $\overline{AB}$. If $\angle AOE = 60^\circ$ and $\angle BOF = 30^\circ$, find the ratio of the area of sector $EOF$ to the area of the circle.

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