
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 the solution set of the inequality ${{x}^{2}}-2x-3 < 0$ is $A$, and the solution set of the inequality ${{x}^{2}}+x-6 < 0$ is $B$.

$(1)$ Find $A\cap B$;

$(2)$ If the solution set of the inequality ${{x}^{2}}+ax+b < 0$ is $A\cap B$, find the values of $a$ and $b$.

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