
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
A plane is passed through the diagonal of the base and the height of a regular quadrangular pyramid. The ratio of the area of the section to the lateral surface area of the pyramid is equal to $k$. Find the cosine of the angle between the slant heights of the opposite lateral faces and the permissible values of $k$.

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