
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 $A=\{x| -2 \lt x \lt 2\}$ and $B=\{x| m-2\leqslant x\leqslant 2m+1\}$.  
$(1)$ When $m=1$, find the set $A\cup B$;  
$(2)$ If sets $A$ and $B$ satisfy: ① $A\cap B=\varnothing$, ② $A\cup B=A$, choose one of the conditions from ① and ②, and find the range of real numbers for $m$.

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