
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 dihedral angles at the base of a pyramid are equal to \(\alpha\), and the angles formed by the lateral edges with the plane of the base are equal to \(\beta\). It is known that \(\operatorname{tg} \alpha = k \operatorname{tg} \beta\). How many sides does the base of the pyramid have if \(k = 2\)? What values can the quantity \(k\) take?

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