
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
Let us cut a regular tetrahedron with a plane that is perpendicular to one of its faces and intersects it at the line $e$. The lines of intersection between this plane and the tetrahedron's other three faces form angles $\varphi_{1}, \varphi_{2}, \varphi_{3}$ with line $e$. Determine the possible values of the expression

$$
\operatorname{tg}^{2} \varphi_{1}+\operatorname{tg}^{2} \varphi_{2}+\operatorname{tg}^{2} \varphi_{3}.
$$

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