
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 the function $f(x) = -tx^2 + 2x + 1$ (where $t < 0$, and $t$ is a constant), for any two different $x_1$, $x_2$, when $x_1$, $x_2 \in [-2, 2]$, it always holds that $|f(x_1) - f(x_2)| \leq k|x_1 - x_2|$ (where $k$ is a constant, $k \in \mathbb{R}$). Then, the range of values for the real number $k$ is.

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