
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 five points \(A, B, C, D,\) and \(E\) in the plane in general position (meaning no three of them are ever collinear, and no four of them are ever cocyclic), a separator is defined as a circle passing through three of these points such that one of the remaining two points lies inside the circle, and the other lies outside. How many separators are there?

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