
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
There are \( n \) light bulbs arranged in a row, and some of them are initially turned on. Each minute, the light bulbs that were on the previous minute turn off, while the off light bulbs that were neighbors to exactly one lit bulb the previous minute turn on. For which values of \( n \) is it possible to initially turn on some of the bulbs such that at any moment afterward there is at least one bulb that is on?

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