
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  $2015$  points on a plane and no two distances between them are equal. We call the closest  $22$  points to a point its  $neighbours$ . If  $k$  points share the same neighbour, what is the maximum value of  $k$ ?

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