
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 lateral edge of a regular quadrilateral pyramid makes an angle \( \alpha \) with the plane of the base. A plane is constructed through a vertex of the base and the midpoint of the opposite lateral edge, parallel to one of the diagonals of the base. Find the angle between this plane and the plane of the base of the pyramid.

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