
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
\[ f(x) = \max \{ -5x - 25, 2x - 2, 7x + 5 \} \]
defined for all real \( x \). Let \( q(x) \) 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