
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 5 points on a plane, where no 3 points are collinear, and no 4 points are concyclic. A circle that passes through any 3 of these points, with one of the remaining 2 points inside the circle and the other point outside, is termed a "good circle." Let $n$ represent the number of good circles. Find all possible values of $n$.

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