
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 $a(x) = 3x + 1$, $b(x) = -2x + 6$, $c(x) = x - 3$. Let $m(x) = \text{avg}\{a(x),b(x),c(x)\}$, which is the average of $a(x)$, $b(x)$, and $c(x)$. What is the squared length of the graph of $y=m(x)$ over the interval $-2 \le x \le 4$?

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