
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
Through the vertex of a cone, a plane is drawn which divides the circumference of the base in the ratio \( p: q \). This plane is at a distance \( a \) from the center of the base of the cone and makes an angle \( \alpha \) with the height of the cone. Find the volume of the cone.

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