
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 defined as follows:
- \(f(x) = -\frac{1}{2}x\) when \(-5 \leq x < 0\)
- \(f(x) = \frac{1}{3}x\) when \(0 \leq x \leq 5\)

On this interval, what is the range of \(f(x) + x\)?

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