
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 $O$ has three points $A$, $B$, and $C$ on its surface, with $BC=3$ and $∠BAC=30^{\circ}$. A cross-section is created by passing through points $A$, $B$, and $C$, and the distance from the sphere's center $O$ to this cross-section is $4$. Calculate the sphere's volume.

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