
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 $M=\{(a+3)+(b^2-1)i, 8\}$ and $N=\{3i, (a^2-1)+(b+2)i\}$, where $M \cap N \subset M$ and $M \cap N \neq \emptyset$, find the integers $a$ and $b$.

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