
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 $f(x)$ is an even function, and for any $x\_1$, $x\_2 \in [0, +\infty]$, the inequality $\frac{f(x\_1) - f(x\_2)}{x\_1 - x\_2} > 0$ holds true ($x\_1 \neq x\_2$), if $f(ax + 1) \leqslant f(2)$ holds true for $x \in [m, n]$, where real numbers $m$ and $n$ satisfy $\frac{m + m}{1 + i} = \frac{3}{4} + \frac{1}{4}i$, then the range of values for the real number $a$ is _______.

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