
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 a piecewise linear function $f(x)$ shown below, consisting of five line segments with the following paths, drawn on a graph where the distance between grid lines is $1$:
- Segment 1 goes from (-5, -4) to (-3, 0).
- Segment 2 moves from (-3, 0) to (-2, -2).
- Segment 3 runs from (-2, -2) to (0, 2).
- Segment 4 extends from (0, 2) to (2, 0).
- Segment 5 spans from (2, 0) to (5, 6).

Determine the sum of the x-coordinates of all points where $f(x) = 3$.

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