
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 regular quadrilateral pyramid, a plane is drawn through two lateral edges that do not belong to the same face. The ratio of the area of the cross-section to the lateral surface area of the pyramid is $k$. Find the angle between two adjacent lateral faces and the permissible values of $\boldsymbol{k}$.

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