
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 graph of a function $y=g(x)$, which consists of three line segments, shown below:
- Segment one goes from $(-3, -3)$ to $(-1, 1)$.
- Segment two goes from $(-1, 1)$ to $(1, -1)$.
- Segment three goes from $(1, -1)$ to $(4, 5)$.

What is the sum of the $x$-coordinates of all points where $g(x) = 2$?
[No graph plot needed for solution text]

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