
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 $f(x) = -x+3$, $g(x) = 0.5x-1$, and $h(x)$ is the constant function $h(x) = 2$. Define $j(x) = \max\{f(x),g(x),h(x)\}$ and $k(x) = \min\{f(x),g(x),h(x)\}$. Find $\ell$, the length of the graph of $y=k(x)$ for the interval $-3 \le x \le 4$ and then compute $\ell^2$.

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