
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 each vertex of the tetrahedron $ABCD$ lies on the surface of the sphere $O$, $CD\bot $ plane $ABC$, $AC=2\sqrt{3}$, $\triangle ABC$ is an equilateral triangle, and $\triangle ACD$ is an isosceles triangle, calculate the volume of sphere $O$.

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