
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 a triangular prism ABC-A₁B₁C₁ whose all vertices are on the surface of a sphere O, the circles obtained by intersecting the sphere with the planes of the five faces of the prism are of the same size, and the surface area of sphere O is 20π, find the volume of the triangular prism.

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