
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
【Reading】We have learned the addition and multiplication rules of rational numbers. When learning this content, we not only mastered the rules but also learned to think in categories.<br/>【Exploration】<br/>$(1)$ If $ab=6$, then the value of $a+b$ is: ① positive, ② negative, ③ $0$. What do you think the result could be? (Fill in the number)<br/>$(2)$ If $a+b=-5$, and $a$ and $b$ are integers, then the maximum value of $ab$ is ______;<br/>【Extension】<br/>$(3)$ On the number line, points $A$ and $B$ correspond to rational numbers $a$ and $b$ respectively. If $ab \lt 0$, compare the sizes of $a+b$ and $0$.

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