
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 $A=\{x|1\leqslant x\leqslant 3\text{ or }4 < x < 6\}$, and set $B=\{x|2\leqslant x < 5\}$, find the following sets:
$(1)\lnot_{U}A$ and $\lnot_{U}B$;
$(2)A\cap(\lnot_{U}B)$;
$(3)(\lnot_{U}A)\cup B$.

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