
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
In a plane, dividing a finite set of points means separating the set into two non-overlapping subsets \( A \) and \( B \), such that there exists a line that does not pass through any point of the set and all points in subset \( A \) are on one side of the line, while all points in subset \( B \) are on the other side. Determine the maximum number of ways to divide a set of \( n \) points in the plane.

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