
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
For any two positive integers, define the operation (represented by the operator ⊕): when both $m$ and $n$ are positive even numbers or both are positive odd numbers, $m⊕n=m+n$; when one of $m$ and $n$ is a positive even number and the other is a positive odd number, $m⊕n=m×n$. For example, $4⊕6=4+6=10$, $3⊕7=3+7=10$, $3⊕4=3×4=12$. Under the above definition, the number of elements in the set $M=\{(a,b)|a⊕b=12, a,b\in\mathbb{N}^*\}$ is __.

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