
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
There are 100 points marked on a circle, painted either red or blue. Some points are connected by segments, with each segment having one blue end and one red end. It is known that no two red points are connected to the same number of segments. What is the maximum possible number of red points?

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