
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 tetrahedron \(ABCD\), point \(E\) is on edge \(AB\) and point \(F\) is on edge \(CD\) such that \(\frac{AE}{EB} = \frac{CF}{FD} = \lambda \quad (0 < \lambda < +\infty)\). Determine the behavior of the function \(f(\lambda) = \alpha_{\lambda} + \beta_{\lambda}\) as a function of \(\lambda\).

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