
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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