
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 a function $y=g(x)$, $-3 \leq x \leq 3$, consists of the following line segments:
- From $x = -3$ to $x = -2$, the graph is a horizontal line one unit above the line $y = x$.
- From $x = -2$ to $x = 0$, the graph is a horizontal line at $y = x$.
- From $x = 0$ to $x = 2$, the graph is a horizontal line one unit below the line $y = x$.
- From $x = 2$ to $x = 3$, the graph is a horizontal line at $y = x$.
Determine the range of $g(x)-x$.

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