
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 $m$, $n$, define an operation "※" as follows: when $m$, $n$ are both even or both odd, $m※n=m+n$; when one of $m$, $n$ is even and the other is odd, $m※n=mn$. Determine the number of elements in the set $M=\{(a,b)|a※b=12, a\in \mathbb{N}^*, b\in \mathbb{N}^*\}$.

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