
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 set $A=\{x|\frac{x-2}{x+1}≤0\}$, set $B=\{x|2m+3 \lt x \lt m^{2}\}$, $m\in R$.<br/>$(1)$ When $m=-2$, find $A\cup B$;<br/>$(2)$ If $A\cap B=B$, find the range of real number $m$.

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