
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 a pyramid is an isosceles triangle with an angle $\alpha$ between the equal sides. The pyramid is placed inside a cylinder such that its base is inscribed in the base of the cylinder, and its apex coincides with the midpoint of one of the cylinder's generating lines. The volume of the cylinder is $V$. Find the volume of the pyramid.

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