
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 function \(f(x)\) defined on the interval \([-2, 2]\) as follows:
\[ f(x) = \begin{cases} 
-x & \text{if } -2 \leq x \leq 0 \\
x-1 & \text{if } 0 < x \leq 2 
\end{cases} \]
Find the range of \(f(x) + x\) for \(-2 \leq x \leq 2\). Express your answer in interval notation.

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