
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 graph of $y=g(x)$ for $-2\le x\le 4$. The graph passes through the points as follows: $(-2, -1)$, $(-1,-1)$, $(0,0)$, $(1,0)$, $(2,1)$, $(3,1)$, and $(4,2)$. Each interval is a line segment connecting consecutive points. Determine the range of $g(x) - x$ on this interval. Express your answer in interval notation.

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