
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 sets $A=\{x|-1\leqslant x\leqslant 2\}$, $B=\{x|m\leqslant x\leqslant m+1\}$  
$(1)$ When $m=-2$, find $\complement_{\mathbb{R}}(A\cup B)$  
$(2)$ If $B\subseteq A$, find the range of the real number $m$.

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