
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 $A=\{x|\frac{x-5}{x-2}≤0\}$, $B=\{x|x^{2}-2ax+a^{2}-1 \lt 0,a\in R\}$.<br/>(1) When $a=2$, find $(\complement _{U}A)\cap (\complement _{U}B)$;<br/>(2) In the case of $A\cap B=B$; (ii) "$x\in A$" is a necessary but not sufficient condition for "$x\in B$"; (iii) $A\cap B=\varnothing$, choose any one of these three conditions and fill in the blank line, if _____, find the range of real number $a$.

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