
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 $A=\{x|x^{2}\geqslant 9\}$, $B=\{x|\frac{x-7}{x+1}\leqslant 0\}$, $C=\{x||x-2| \lt 4\}$.  
$(1)$ Find $B$ and $C$;  
$(2)$ If the universal set $U=R$, find $A\cup (\complement _{U}B)$.

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