
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 the distance from the center O of a sphere to a plane passing through three points A, B, and C on the surface of the sphere is equal to half the radius of the sphere, and AB=3, $\tan \angle ACB = -\sqrt{3}$, then the volume of sphere O is \_\_\_\_\_\_.

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