
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 $L_1, L_2, \dots, L_{120}$ are distinct. All lines $L_{5n}$, where $n$ is a positive integer, are parallel to each other. All lines $L_{5n-4}$, where $n$ is a positive integer, pass through a given point $B$. Additionally, all lines $L_{5n-2}$ are perpendicular to lines $L_{5n}$. Determine the maximum number of points of intersection of pairs of lines from the complete set $\{L_1, L_2, \dots, L_{120}\}$.
A) 4151
B) 4761
C) 5161
D) 6250

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