
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
Kolya drew 10 line segments and marked all their intersection points in red. After counting the red points, he noticed the following property: on each segment, there are exactly three red points. 
a) Provide an example of the arrangement of 10 line segments with this property.
b) What can be the maximum number of red points for 10 segments with this property?

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