
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 $U=\mathbb{R}$, let the set $A=\{x|x<-4 \text{ or } x>1\}$, $B=\{x|-3 \leq x-1 \leq 2\}$,
(i) Find $A \cap B$ and $(\complement_U A) \cup (\complement_U B)$;
(ii) If $\{x|2k-1 \leq x \leq 2k+1\} \subseteq A$, find the range of the real number $k$.

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