
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 $y=g(x)$, consisting of the following line segments: $y=3x - 3$ from $x=-2$ to $x=0$, $y=-2x$ from $x=0$ to $x=1$, $y=4x-2$ from $x=1$ to $x=3$. What is the sum of the $x$-coordinates of all points where $g(x) = 2$?

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