
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
Fifteen points are selected on the positive $x$-axis, and ten points are selected on the positive $y$-axis. A segment is drawn from each point on the positive $x$-axis to each point on the positive $y$-axis such that no three segments are concurrent at a point other than the axes' intersection. What is the maximum number of points of intersection of these segments within the first quadrant?
A) 3000
B) 3725
C) 4500
D) 4725
E) 5250

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