
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 acute angle of the rhombus at the base of a quadrilateral pyramid is $\alpha$. The ratio of the total surface area of the pyramid to the square of the side of the base is $k$. Find the sine of the angle between the slant height and the height of the pyramid, given that all its lateral faces are equally inclined to the base plane. What are the permissible values of $k$?

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