
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 the function $f(x)$ have a domain of $\mathbb{R}$, and for any real numbers $x$, $y$, it holds that $f(x+y)=f(x)+f(y)$. Also, when $x>0$, $f(x)<0$ and $f(2)=-1$. Does the function $f(x)$ have a maximum and minimum value on the interval $[-6,6]$? If it exists, find the maximum and minimum values; if not, please explain why.

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