
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
Given that \( y = f(x) \) is a monotonous function defined on \(\mathbb{R}\), with real numbers \( x_{1} < x_{2} \), \(\lambda \neq -1\), \(\alpha = \frac{x_{1} + \lambda x_{2}}{1 + \lambda}\), and \(\beta = \frac{x_{2} + \lambda x_{1}}{1 + \lambda}\). If \(\left| f(x_{1}) - f(x_{2}) \right| < |f(\alpha) - f(\beta)|\), find the range of values for \(\lambda\).

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