
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
Given \( n \) squares on a plane, where:

1. All the squares are congruent.
2. If two squares share a common intersection point \( P \), then \( P \) must be a vertex of each of the squares.
3. Any square intersects exactly three other squares.

The collection of these \( n \) squares is called "three-connected."

Determine the number of integers \( n \) within the range \( 2018 \leq n \leq 3018 \) for which there exists a three-connected set of \( n \) squares.

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