
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 \(y=g(x)\) for \(-3\le x\le 3\) defined segment-wise as follows:
- \(g(x) = x + 1\) for \(-3 \leq x < -1\) 
- \(g(x) = x - 1\) for \(-1 \leq x \leq 1\) 
- \(g(x) = x + 1\) for \(1 < x \leq 3\) 

On this interval, what is the range of \(g(x)-x\)?

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