
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
We consider 2018 lines on the plane, each pair of which are not parallel and no three of which are concurrent. Let $E$ be the set of their intersection points. We wish to assign a color to each point in $E$ such that any two points on the same line, whose connecting segment does not contain any other point from $E$, have different colors.

How many colors are needed at minimum to achieve such a coloring?

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