
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
The base of the pyramid is a right triangle with an acute angle $\alpha$. This triangle is inscribed in the base of a cone. The vertex of the pyramid coincides with the midpoint of one of the generatrices of the cone. Find the ratio of the volume of the cone to the volume of the prism.

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