
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 placed on the positive $x$-axis and ten points are placed on the positive $y$-axis. Segments are drawn connecting every point on the $x$-axis to every point on the $y$-axis. Determine the maximum possible number of points of intersection of these segments that could lie strictly within the first quadrant.
A) 2250  
B) 3150  
C) 4725  
D) 5250  
E) 6250

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