
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 base of a pyramid is an equilateral triangle with side \( a \). Two lateral faces of the pyramid are perpendicular to the base, and the equal lateral edges form an angle \( \alpha \) with each other. Find the height of a right triangular prism that is equal in volume to the given pyramid and shares the same base.

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