
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
Consider the function
\[
f(x) = \max \{-7x - 10, 2x - 3, 5x + 4\}
\]
defined for all real \(x\). Let \(p(x)\) be a quadratic polynomial tangent to the graph of \(f\) at three distinct points with \(x\)-coordinates \(x_1\), \(x_2\), \(x_3\). Find \(x_1 + x_2 + x_3\).

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