
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 four linear segments, shown in the plot. The segments are defined as follows:
1. From \( x = -5 \) to \( x = -3 \), with endpoints \((-5, -4)\) and \((-3, 0)\).
2. From \( x = -3 \) to \( x = 0 \), with endpoints \((-3, 0)\) and \( (0, -3) \).
3. From \( x = 0 \) to \( x = 3 \), with endpoints \((0, -3)\) and \((3, 3)\).
4. From \( x = 3 \) to \( x = 5 \), with endpoints \((3, 3)\) and \((5, 0)\).

Calculate the sum of the \( x \)-coordinates of all points where \( g(x) = 0 \).

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