
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
The graph of $y=f(x)$ for $-4\le x\le 4$ is given by a piecewise linear function. The points $(-4, -2)$, $(-3, -3)$, $(-2, -1)$, $(0, 0)$, $(2, 1)$, $(3, 2)$, and $(4, 2)$ are connected sequentially. On this interval, what is the range of $f(x)-x^2$? Express your answer in interval notation.

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