
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
Consider that $p(x), q(x), r(x)$ are all linear functions defined by $p(x) = -\frac{3}{2}x + 1$, $q(x) = \frac{3}{2}x + 1$, $r(x) = 2$. Define $m(x) = \min\{p(x), q(x), r(x)\}$ and $n(x) = \max\{p(x), q(x), r(x)\}$. Find the value of $s^2$, where $s$ is the length of the graph of $y=m(x)$ for $-4\le x\le 4$.

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