
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
(This question is worth 8 points)

It is known that the function $f(x)$, for any real numbers $x$ and $y$, satisfies $f(x+y) = f(x) + f(y)$, and when $x>0$, $f(x)>0$, $f(-1)=-2$. Find the range of $f(x)$ on the interval $[-2, 1]$.

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