
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
\( M \) is a set of points on a plane. A point \( O \) is called an "almost center of symmetry" of the set \( M \) if one point can be removed from \( M \) so that \( O \) becomes the center of symmetry for the remaining set in the usual sense. How many "almost centers of symmetry" can a finite set on the plane have?

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