
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 sphere is placed inside a cone such that their surfaces touch each other. The radius of the sphere is \( R \), and the angle at the vertex of the axial section of the cone is \( 2\alpha \). Find the volume of the region bounded by the surfaces of the sphere and the cone.

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