
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
The proposition $p$: The circle $M: (x^2 + y^2 - 2ax - 2ay + 2a^2 - 2 = 0) (a \in R)$ has no common points with the circle $O: x^2 + y^2 = 18$. If $\neg p$ is a true proposition, the maximum value of the distance between the center $M$ of circle $M$ and point $N(1, 2)$ is $\_\_\_\_\_$.

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