
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 busy bee buzzes between the cells of a large honeycomb made up of a plane of tessellated hexagons. A flight of length \( n \) consists of picking any of the six neighboring cells and flying to the \( n^{\text{th}} \) cell in that direction. After consecutive flights of lengths \( n=N, N-1, \ldots, 2, 1 \), the bee finds that it has returned to its starting location. For which values of \( N \) is this possible?

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