
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 $U = \mathbb{R}$, set $A=\{x|\frac{x-5}{x-2}≤0\}$, $B=\{x|a-1 \lt x \lt a+1, a\in \mathbb{R}\}$.  
$(1)$ When $a=2$, find $(\complement _{U}A)\cap (\complement _{U}B)$;  
$(2)$ If $x\in A$ is a necessary but not sufficient condition for $x\in B$, find the range of real numbers $a$.

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