
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
\[g(x) = \max \{-7x - 21, 2x - 6, 4x + 12\}\]defined for all real $x.$ Let $q(x)$ be a quadratic polynomial tangent to the graph of $g$ 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}
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