
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
Lines $L_1, L_2,\dots,L_{150}$ are distinct. All lines $L_{5n}, n$ a positive integer, are parallel to each other. All lines $L_{5n-4}, n$ a positive integer, pass through a given point $A.$ All lines $L_{5n-2}, n$ a positive integer, are perpendicular to line $L_1$. You need to calculate the maximum number of points of intersection of pairs of lines from the complete set $\{L_1, L_2, \dots, L_{150}\}$.
A) 4351  
B) 9851  
C) 9871  
D) 9900

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