
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
The complete graph of $y=g(x)$, which consists of four line segments, is shown below. Find the sum of the $x$-coordinates of all points where $g(x) = 2.5$. The equations of the line segments, from left to right, are:
1. $y = 3x + 6$ for $-4 \leq x \leq -2$,
2. $y = -x + 2$ for $-2 < x \leq 0$,
3. $y = 2x - 2$ for $0 < x \leq 3$,
4. $y = -2x + 8$ for $3 < x \leq 5$.

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