
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 universal set $R$, set $A=\{x|x^{2} \lt 4\}$, $B=\{x\left|\right.\left(x-m-1\right)\left(x-m-7\right) \gt 0\}$.  
$(1)$ If $m=-2$, find the set $A\cup \complement _{R}B$;  
$(2)$ Please choose one of the following conditions: in ① "$x\in A$" implies "$x\in B$", ② if $x\in A$, then $x\notin B$, ③ $A\subseteq \complement _{R}B$, and complete the blank line below the question. Find the range of real numbers for $m$ if _____.

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