
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 with an acute angle between the equal sides of $\alpha$. All lateral edges form the same angle $\beta$ with the plane of the base. A plane is drawn through the side of the base opposite the angle $\alpha$ and the midpoint of the height of the pyramid. Find the angle between this plane and the plane of the base.

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