
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 $p:x\in A$, where $A=\{x|a-1 \lt x \lt a+1\}$, and $q:x\in B$, where $B=\{x|x\geqslant 3$ or $x\leqslant 1\}$.  
$(1)$ If $A\cap B=\varnothing$, $A\cup B=R$, find the value of the real number $a$;  
$(2)$ If $p$ is a sufficient condition for $q$, find the range of values for the real number $a$.

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