
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 an integer $n \geqslant 1$, Élodie wants to draw $n$ rectangles $R_{1}, R_{2}, \ldots, R_{n}$ with sides that are vertical and horizontal. Two rectangles $R_{i}$ and $R_{j}$ are said to meet if they have at least one point in common (even on their edge), and they are said to follow each other if $i \equiv j \pm 1 \bmod n$.

For which integers $n$ can Élodie draw these $n$ rectangles such that two rectangles meet if and only if they do not follow each other?

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