
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 $A=\{x||x-2|\geqslant 1\}$, and set $B=\{x|k < x < 2k+1\}$,

(1) Find $A\cap B$ when $k=2$,

(2) Determine the range of values for the real number $k$ such that $(\lnot_{U}A)\cap B=\varnothing$.

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