
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 that the function $f(x)$ satisfies $f(x+y)=f(x)+f(y)$ for all real numbers $x$, $y\in\mathbb{R}$, and $f(x) < 0$ when $x > 0$, with $f(3)=-2$.

(1) Determine the parity (odd or even) of the function.
(2) Determine the monotonicity of the function on $\mathbb{R}$.
(3) Find the maximum and minimum values of $f(x)$ on $[-12,12]$.

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