
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 distance from the vertex of the base of a regular tetrahedral pyramid to the opposite lateral face is \( l \). The angle between the lateral face and the base plane of the pyramid is \( \alpha \). Find the total surface area of the cone inscribed in the pyramid.

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