
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 piecewise function \(f(x)\) defined as follows on the interval \([-4, 4]\):
\[
f(x) = \begin{cases} 
x + 2 & \text{for } -4 \leq x \leq -1 \\
-x & \text{for } -1 < x < 2 \\
x - 1 & \text{for } 2 \leq x \leq 4
\end{cases}
\]
Determine the range of the expression \(f(x) - x\) over the given interval. Express your answer in interval notation.

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