
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
In a pyramid with all lateral faces equally inclined to the base plane, a plane parallel to the base is passed through the center of the inscribed sphere. The ratio of the area of the section of the pyramid by this plane to the area of the base is $k$. Find the dihedral angle at the base of the pyramid.

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