
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 that sets $A$ and $B$ are subsets of $N^{*}$, where $A$ and $B$ each contain at least two elements, and $A$ and $B$ satisfy: 
For any $x$, $y\in A$, if $x\neq y$, then $xy\in B$; For any $x$, $y\in B$, if $x \lt y$, then $\frac{y}{x}∈A$. If $A$ contains $4$ elements, determine the number of elements in $A\cup B$.

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