
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 \(y=g(x)\) given by the following piecewise definition for \(-3 \leq x \leq 3\):
\[ g(x) = 
  \begin{cases} 
    -x-1 & \text{for } -3 \leq x < -1 \\
    x & \text{for } -1 \leq x \leq 2 \\
    5-x & \text{for } 2 < x \leq 3
  \end{cases} 
\]
Determine the range of \(g(x) - x\) over the interval \(-3 \leq x \leq 3\), and express your answer in interval notation.

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