
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 inscribed in a cone, and a tangent plane is drawn to the sphere, parallel to the base plane of the cone. In what ratio does this plane divide the lateral surface of the cone, if the angle between the generatrix and the base plane is $\alpha$?

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