
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
All lateral faces of a pyramid form the same angle with the plane of the base. Find this angle if the ratio of the total surface area of the pyramid to the area of the base is $k$. For which values of $k$ does the problem have a solution?

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