
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
Suppose $p(x), q(x), r(x)$ are linear functions defined as $p(x) = 2x + 1$, $q(x) = -x + 3$, and $r(x) = 0.5x + 2$. Define new functions $u(x)$ and $v(x)$ by
$$u(x) = \max\{p(x), q(x), r(x)\},$$
$$v(x) = \min\{p(x), q(x), r(x)\}.$$
Calculate the squared length of the graph of $y = v(x)$ for $-4 \leq x \leq 4$.

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