
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
Consider  $n \geq 2$  distinct points in the plane  $A_1,A_2,...,A_n$  . Color the midpoints of the segments determined by each pair of points in red. What is the minimum number of distinct red points?

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