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

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