
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 by \( p(x) = ax + b \), \( q(x) = cx + d \), \( r(x) = ex + f \) where \( a, c, e \) are slopes and \( b, d, f \) are y-intercepts. Define \( s(x) = \max\{p(x),q(x),r(x)\} \) and \( t(x) = \min\{p(x),q(x),r(x)\} \). Consider the graph of \( y = s(x) \) for the interval \([-4, 4]\).

Calculate the square of the length \( m^2 \) of the graph \( y = t(x) \) for the same interval assuming:
\[ p(x) = 2x + 1, \]
\[ q(x) = -x + 4, \]
\[ r(x) = x + 3. \]

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