
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
Find the angle between the apothem of a regular triangular pyramid and the plane of its base, if the difference between this angle and the angle that the lateral edge of the pyramid makes with the plane of the base is equal to $\alpha$.

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