
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 $U=\mathbb{R}$, $A=\{x|x<-2 \text{ or } x>5\}$, $B=\{x|4\leq x\leq 6\}$, find $\complement_UA$, $\complement_UB$, $A\cap B$, and $\complement_U(A\cup B)$.

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