
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
Choose one of the following three conditions:  
① $A=\left\{x|{{\log}_{\frac{1}{2}}}(x+1) \geq -2\right\}$;  
② $A=\left\{x|\frac{1}{8} \leq {(\frac{1}{2})}^x < 2\right\}$;  
③ $A=\left\{x|\frac{{3x-1}}{{x+1}} \leq 2\right\}$  
Given the set ____, set $B=\{x|2m < x < m^{2}$, $m\in R\}$.  
$(1)$ When $m=-1$, find $A\cup B$;  
$(2)$ Let proposition $p:x\in A$, proposition $q:x\in B$, $p$ is a necessary but not sufficient condition for $q$, find the range of real number $m$.

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