
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
If the function $f(x) = 2^{|x+a|}$ (where $a\in\mathbb{R}$) satisfies $f(1-x) = f(1+x)$, and the maximum and minimum values of $f(x)$ on the interval $[m, n]$ are denoted as $f(x)_{\text{max}}$ and $f(x)_{\text{min}}$ respectively, and $f(x)_{\text{max}} - f(x)_{\text{min}} = 3$, then the range of values for $n-m$ is ______.

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