
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 that circle O's diameter AB, angle AOE is 60 degrees, and angle FOB is 90 degrees, find the ratio of the area of the smaller sector EOF to the area of the circle.

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