
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 $U=\{x|x$ is a positive integer less than $9\}$, $A=\{1,2,3\}$, $B=\{3,4,5,6\}$. Find:<br/>
$(1)\complement _{U}A$;<br/>
$(2)\complement _{U}B$;<br/>
$(3)B\cap (\complement _{U}A)$;<br/>
$(4)A\cup (\complement _{U}B)$.

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