
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 interval with endpoints at red points that contains a red point inside, there are at least 4 blue points. Additionally, on any interval with endpoints at blue points that contains 3 blue points inside, there are at least 2 red points. What is the maximum number of blue points that can be on an interval with endpoints at red points, not containing other red points inside?

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