
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 $y=g(x)$, presented by three line segments, is shown below. The graph segments are as follows: from $(-4, -6)$ to $(-1, -1)$, then from $(-1, -1)$ to $(1, 1)$, and from $(1, 1)$ to $(4, 6)$. Assume the distance between grid lines is $1$.

Determine the sum of the $x$-coordinates of all points where $g(x) = x^2 - 2$.

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