
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 isosceles triangle whose area is \( S \) and the angle between the equal sides is \( \alpha \). All the lateral edges of the pyramid make the same angle with the plane of the base. Find this angle if the volume of the pyramid is \( V \).

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