
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 $f(x) = 2x + 1$, $g(x) = -x + 4$, and $h(x) = 3$. Let $j(x) = \max\{f(x), g(x), h(x)\}$ and $k(x) = \min\{f(x), g(x), h(x)\}$ over the interval $-2 \leq x \leq 3$. Calculate the square of the length $\ell$ of the graph of $y = k(x)$ over this interval.

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