
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 set $A=\{x|y= \dfrac {1}{ \sqrt {2^{x}-1}}\}$, and set $B=\{x|y=\ln (x^{2}-x-6)\}$  
$(1)$ Find the intersection of sets $A$ and $B$;  
$(2)$ If the solution set of the inequality $ax^{2}+2x+b > 0$ is $A\cup B$, find the values of $a$ and $b$.

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