
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 $A=\{x|x^{2}-x-6 \lt 0\}$, $B=\{x|x>-3 \text{ and } x\leqslant 3\}$.  
$(1)$ Find the set $A$;  
$(2)$ Find $\complement _{R}(A \cap B)$ and $(\complement _{R}A) \cap B$.

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