
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 $A=\{x\mid-1\leqslant x < 3\}$, and set $B=\{x\mid x-k\leqslant 0\}$,
(1) If $k=1$, find $A\cap \lnot_{U}B$
(2) If $A\cap B\neq \varnothing$, find the range of values for $k$.

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