
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 $A=\{x|{\frac{{x-1}}{{x-5}}＜0}\}$ and $B=\{x|x^{2}-2ax+a^{2}-1 \lt 0\}$.<br/>$(1)$ If $a=1$, find $A\cup B$;<br/>$(2)$ If $A\subseteq \complement _{R}B$, find the range of real number $a$.

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