
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 $A=\{x|\frac{x+2}{x-\frac{3}{2}}＜0\}$ and $B=\{x|{x}^{2}-(m+1)x+m≤0\}$.<br/>$(1)$ When $m=2$, find $A\cup B$;<br/>$(2)$ Given that "$x\in A$" is a sufficient condition for "$x\in B$", find the range of real number $m$.

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