
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,$X^+$, and ten points are selected on the positive $y$-axis,$Y^+$. The one hundred fifty segments connecting the fifteen points on $X^+$ to the ten points on $Y^+$ are drawn. What is the maximum possible number of points of intersection of these one hundred fifty segments that could lie in the interior of the first quadrant?
A) 3000
B) 3500
C) 4000
D) 4725
E) 5000

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