
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 $U=\{x\in\mathbb{N}\ |\ 0<x\leq 6\}$, set $A=\{x\in\mathbb{N}\ |\ 1<x<5\}$, and set $B=\{x\in\mathbb{N}\ |\ 2<x<6\}$. Find:
(1) $A\cap B$
(2) $(C_U A)\cup B$
(3) $(C_U A)\cap (C_U B)$

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