
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 quadratic functions defined as $p(x) = x^2 - x + 1$, $q(x) = -x^2 + 3x + 4$, and $r(x) = 2x^2 - 5x + 6$. Let $m(x) = \max\{p(x), q(x), r(x)\}$ and $n(x) = \min\{p(x), q(x), r(x)\}$.
Calculate the length of the graph of $y = n(x)$ from $x = -2$ to $x = 2$.

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