
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 six points are selected on the positive $y$-axis, \( Y^+ \). All possible segments connecting points from \( X^+ \) to \( Y^+ \) are drawn. What is the maximum possible number of points of intersection of these segments that could lie in the interior of the first quadrant if none of the points on \( Y^+ \) have an integer coordinate?

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