
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 that there are two points on the circle $C: x^{2}+y^{2}-2nx+2ny+2n^{2}-8=0$ such that the distance from these points to point $A(-1,1)$ is both $\sqrt{2}$, one possible value of the real number $n$ is ______.

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