
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 $A=\{x|x^{2}-2x-3 < 0\}$, $B=\{x|x^{2}-5x+6 < 0\}$.  
$(1)$ Find $A\cap B$;  
$(2)$ If the solution set of the inequality $x^{2}+ax+b < 0$ is $A\cap B$, find the solution set of $x^{2}+ax-b < 0$.

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