
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 sets $A=\{1,2,3,4\}$ and $B=\{2,4,6,8\}$, define the set $A\times B=\{(x,y)|x\in A, y\in B\}$. The number of elements in the set $A\times B$ that belong to the set $\{(x,y)|\log_{x}y \in \mathbb{N}\}$ is ______.

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