
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 \(A=\left\{x \left\lvert\, \frac{1}{81}<3^{x-1} \leqslant 3\right., x \in \mathbf{Z}\right\}\) and \(B=\left\{x \left\lvert\, \frac{x+2}{x-3}<0\right., x \in \mathbf{N}\right\}\), find the number of elements in the set \(C=\{m \mid m=x y, x \in A, y \in B\}\).

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