
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 $L_{5n}, n$ a positive integer, are parallel to each other.
All lines $L_{5n-4}, n$ a positive integer, pass through a given point $P$. Additionally, all lines $L_{3n-2}, n$ a positive integer, pass through another given point $Q$. Determine the maximum number of points of intersection of pairs of lines from the set $\{L_1,L_2,\dots,L_{120}\}$.
A) 6500
B) 6570
C) 6589
D) 6600
E) 6630

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