
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 \( y = g(x) \) from \(-4 \leq x \leq 4\) consists of line segments and points. Determine the range of \( g(x) - x \). The graph is defined by the set of points and segments as follows:

- \( (-4, -2) \), filled dot.
- \( (-3, -3) \), filled dot.
- Segment joining \( (-4, -2) \) to \( (-3, -3) \) but not including \( (-3, -3) \).
- \( (-3, -3) \) to \( (0,0) \), continuous line segment, including both endpoints.
- \( (0, 0) \) to \( (2, 3) \), includes both endpoints.
- \( (2, 3) \) to \( (3, 3) \), includes both endpoints.
- \( (3, 3) \) to \( (4, 2) \), includes both endpoints.

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