
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 that 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 $A∩B$; (Note: $A∩B={x|x∈A且x∈B}$)

(2) If the solution set of the inequality $-{{x}^{2}}+bx+c > 0$ is $A∩B$, find the solution set of the inequality $c{{x}^{2}}+bx-1 > 0$.

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