
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
A sphere with radius 1 has its center at point \( O \). From a point \( A \), located outside the sphere, four rays are drawn. The first ray intersects the surface of the sphere at points \( B_1 \) and \( C_1 \) sequentially, the second ray at points \( B_2 \) and \( C_2 \), the third ray at points \( B_3 \) and \( C_3 \), and the fourth ray at points \( B_4 \) and \( C_4 \). Lines \( B_1B_2 \) and \( C_1C_2 \) intersect at point \( E \), and lines \( B_3B_4 \) and \( C_3C_4 \) intersect at point \( F \). Find the volume of pyramid \( OAEF \), given \( AO = 2 \), \( EO = FO = 3 \), and the angle between faces \( AOE \) and \( AOF \) is \( 30^\circ \).

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