
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 $U=\mathbb{R}$, the set $A=\{x|x\leqslant 1\}$ or $x\geqslant 3\}$, and the set $B=\{x|k < x < 2k+1\}$. It is also given that $(\complement_{U}A)\cap B=\varnothing$. Find the range of the real number $k$.

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