
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 set $A=\{x|x\leq1 \text{ or } x\geq3\}$, and the set $B=\{x|k<x<k+1\}$, where $k\in \mathbb{R}$, if $(C_{\mathbb{R}}A) \cap B = \varnothing$, determine the range of $k$.

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