
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, two red points and several blue points are marked. It turns out that one of the red points is contained in exactly 56 segments with blue endpoints, and the other red point is contained in 50 segments with blue endpoints. How many blue points are marked?

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