
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
If the elements in sets $A$ and $B$ are all non-zero real numbers, and $A\otimes B=\left\{{x|x=\frac{m}{n},m∈A,n∈B}\right\}$, if $A=\left\{{a,\sqrt{2},2}\right\}$, $B=\left\{{\sqrt{2},2}\right\}$, and there are $4$ elements in $A\otimes B$, calculate the value of $a$.

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