
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 height of a regular triangular truncated pyramid is \( H \) and it is the geometric mean between the sides of the bases. The lateral edge makes an angle \( \alpha \) with the base. Find the volume of the pyramid.

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