
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
In a city, 2019 metro stations have been constructed. Some pairs of stations are connected by tunnels, and it is possible to travel from any station to any other station via these tunnels. The mayor has ordered the organization of several metro lines: each line must include multiple distinct stations connected sequentially by tunnels (one tunnel can be part of multiple lines). Additionally, each station must be part of at least one line. To save costs, the number of lines should be no more than $k$.

It turned out that the mayor's order is impracticable. What is the largest $k$ for which this could happen?

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