
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
On a line, there are blue and red points, with at least 5 red points. It is known that on any segment with endpoints at red points that includes at least one red point inside, there are at least 3 blue points. Additionally, on any segment with endpoints at blue points that includes exactly 2 blue points inside, there are at least 2 red points. What is the maximum number of blue points that can be on a segment with endpoints at red points, not containing other red points?

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