
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 sets $A=\{x|2m-1\leqslant x\leqslant m+2\}$, $B=\{x|-1 \lt x\leqslant 2\}$, $U=R$.  
$(1)$ When $m=-1$, find:  
① $A\cup B$  
② $A\cap (\complement _{U}B)$  

$(2)$ If $A\cap B=\varnothing$, find the range of real number $m$.

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