
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
There are  $2019$  points given in the plane. A child wants to draw  $k$  (closed) discs in such a manner, that for any two distinct points there exists a disc that contains exactly one of these two points. What is the minimal  $k$ , such that for any initial configuration of points it is possible to draw  $k$  discs with the above property?

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