
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
One lateral edge of a triangular pyramid is perpendicular to the base plane and has length \( l \). The other two lateral edges form an angle \( \alpha \) with each other and both form the same angle \( \beta \) with the base plane. Find the volume of the pyramid.

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