
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 all real numbers $x, y \in \mathbb{R}$, it satisfies $f(x+y) = f(x) + f(y)$, and when $x > 0$, $f(x) < 0$. Also, $f(3) = -2$.
1. Determine the parity (evenness or oddness) of the function;
2. Determine the monotonicity of the function on $\mathbb{R}$;
3. Find the maximum and minimum values of $f(x)$ on the interval $[-12, 12]$.

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