
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 hemisphere is inscribed in a cone such that the great circle of the hemisphere lies in the plane of the base of the cone, and the spherical surface touches the surface of the cone. Find the volume of the hemisphere if the slant height of the cone is \( l \) and it forms an angle \( \alpha \) with the plane of the base.

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