
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 $A=\{x|x\in\mathbb{R}, (x-2)(x-6)\leqslant 0\}$, $B=\{x|x\in\mathbb{R}, x^{2}-6x+5 \lt 0\}$, $C=\{x|x\in\mathbb{R}, m \lt x \lt m+1\}$, $U=\mathbb{R}$.  
$(1)$ Find $A\cup B$, $(\complement _{U}A)\cap B$;  
$(2)$ If $C\subseteq B$, find the range of values for $m$.

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