
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
Given the function \( f(x) \) defined for \( -4 \leq x \leq 4 \) by the following piecewise segments: \( f(x) = -x-1 \) for \( -4 \leq x \leq -3 \), \( f(x) = -x \) for \( -3 < x \leq 3 \), and \( f(x) = -x+1 \) for \( 3 < x \leq 4 \), find the range of \( f(x) - 2x \).

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