
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
Let the graph of \( y = f(x) \) for \(-5 \leq x \leq 5\) be a piecewise-linear function defined as follows:
- \( f(x) = -x \) if \( -5 \leq x \leq -1 \)
- \( f(x) = -1 \) if \( -1 < x \leq 1 \)
- \( f(x) = x \) if \( 1 < x \leq 5 \)

Determine the range of \( f(x) - x \) for the domain \(-5 \leq x \leq 5\). Express your answer in interval notation.

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