
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 graph of \( y = g(x) \) for \( -4 \leq x \leq 4 \), determine the range of \( g(x) - 2x \). The graph of \( y = g(x) \) is as follows, with \( g(x) \) defined piecewise linearly through points \( (-4, -2) \), \( (-2, -1) \), \( (0, 0) \), \( (2, 3) \), and \( (4, 4) \).

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