
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 that the universal set $U=R$, and sets $A={x||x-a|\\leqslant 1}$, $B={x|(4-x)(x-1)\\leqslant 0}$.
(1) If $a=4$, find $A∪B$;
(2) If $A∩B=A$, find the range of values for the real number $a$.

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