
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
A collection of  $n$  squares on the plane is called tri-connected if the following criteria are satisfied:

(i) All the squares are congruent.
(ii) If two squares have a point  $P$  in common, then  $P$  is a vertex of each of the squares.
(iii) Each square touches exactly three other squares.

How many positive integers  $n$  are there with  $2018\leq n \leq 3018$ , such that there exists a collection of  $n$  squares that is tri-connected?

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