
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 15 red points on a plane. Lines are drawn between some of these red points. A red point is marked with the number of lines connected to it. It is known that all points marked with the same number are not connected to each other. What is the maximum number of lines that can be drawn between these 15 red points?

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