
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 a right triangle with one of its acute angles equal to $\alpha$. All the lateral edges are equally inclined to the plane of the base. Find the dihedral angles at the base, given that the height of the pyramid is equal to the hypotenuse of the triangle forming the base.

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