
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 universal set $U = R$, set $A=\{x| m-1 \lt x \lt 2m+1\}$, $B=\{x|\frac{x-7}{x-2}＜0\}$.  
$(1)$ When $m=2$, find $A\cap (\complement _{U}B)$;  
$(2)$ If $A\cup B=B$, find the range of values for $m$.

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