
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
Let the universal set $U=\{x\in\mathbb{N}^*|x<9\}$, $A=\{1,2,3\}$, $B=\{3,4,5,6\}$.

(1) Find $A\cup B$, $A\cap B$, $C_U(A\cup B)$, $C_U(A\cap B)$;  
(2) Find $C_UA$, $C_UB$, $(C_UA)\cup(C_UB)$, $(C_UA)\cap(C_UB)$;

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