
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
Let $f(x)$ be an odd function which satisfies the equation $f(x + y) = f(x) + f(y)$ for all $x, y \in \mathbb{R}$. In addition, for $x > 0$, it holds that $f(x) < 0$. If $f(1) = -2$, find the maximum and minimum values of $f(x)$ on the interval [-3, 3].

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