
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 set $A=\{x|0\leqslant x-1\leqslant 2\}$, and $R$ is the set of real numbers, $B=\{x|1 < x-a < 2a+3\}$.  
(I) When $a=1$, find $A\cup B$ and $A\cap \complement_R B$;  
(II) If $A\cap B\neq \varnothing$, find the range of values for $a$.

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