
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 regular tetrahedron is inscribed in a cylinder such that two opposite edges of the tetrahedron are the diameters of the cylinder's bases. Find the ratio of the volume of the cylinder to the volume of the tetrahedron.

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