
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
Given 2017 lines separated into three sets such that lines in the same set are parallel to each other, what is the largest possible number of triangles that can be formed with vertices on these lines?

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