
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
Given a pyramid \( S A B C \) with a triangular base \( A B C \) that is equilateral, and all the plane angles at the vertex \( S \) are equal to \( \alpha \). What is the smallest \( \alpha \) for which we can claim that this pyramid is regular?

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