
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 $f(x)$ defined piecewise by the following line segments: $(-4, -3)$ to $(-2,1)$, $(-2,1)$ to $(0,-2)$, $(0,-2)$ to $(2, 3)$, $(2,3)$ to $(4,0)$. The goal is to find the sum of the $x$-coordinates of all points where $f(x) = 2.5$.

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