
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 ratio of the area of the diagonal cross-section of a regular quadrilateral pyramid to the area of its base is equal to \( k \). Find the cosine of the planar angle at the apex of the pyramid.

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