
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
The lines \( L_{1}, L_{2}, \cdots, L_{100} \) are distinct, with all lines \( L_{4n} \) being parallel to each other (where \( n \) is a positive integer) and all lines \( L_{4n-3} \) passing through a known point \( A \) (where \( n \) is a positive integer).

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