
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 a finite set of points $S$ in a plane with at least 3 points, for any two distinct points $A$ and $B$ in $S$, the perpendicular bisector of the segment $AB$ is an axis of symmetry of the set $S$. Find all such point sets $S$.

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