
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 universal set $U=\mathbb{R}$, set $A=\{x|x < -4 \text{ or } x > 1\}$, $B=\{x|-3\leqslant x-1\leqslant 2\}$,
(I) Find $A\cap B$, $(∁_{U}A)\cup(∁_{U}B)$;
(II) If $\{x|2k-1\leqslant x\leqslant 2k+1\}\subseteq A$, find the range of values for the real number $k$.

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