
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 $L_1, L_2, \dots, L_{100}$ are distinct. Lines $L_{5n}$ for integers $n$, are parallel to each other. Lines $L_{5n-4}$ for integers $n$, pass through a given point $B$. The maximum number of points of intersection of pairs of lines from the set $\{L_1, L_2, \dots, L_{100}\}$ is to be calculated.
**A)** 4570
**B)** 4571
**C)** 4851
**D)** 5000

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