
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 a function $f(x)$ such that for any $x, y \in \mathbb{R}$, it holds that $f(x+y) = f(x) + f(y)$, and $f(x) < 0$ when $x > 0$, $f(1) = -2$.

1. Determine the parity (odd or even) of the function $f(x)$.
2. Does the function $f(x)$ have a maximum or minimum value when $x \in [-3, 3]$? If so, identify the extreme values; if not, explain why.

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