
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
Connecting 10 points on the positive x-axis and 5 points on the positive y-axis to form 50 line segments in the first quadrant, determine the maximum number of intersection points of these 50 line segments within the first quadrant.

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