
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 graph of $y=g(x)$ consists of the following segments, shown in red: $(-5, -3)$ to $(-3, 0)$, $(-3, 0)$ to $(0, -3)$, $(0, -3)$ to $(3, 1)$, $(3, 1)$ to $(4, 0)$, and $(4, 0)$ to $(6, 3)$. Determine the sum of the $x$-coordinates of all points where $g(x) = x + 1$.

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