
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
1. For which natural numbers \( n > 2 \) does there exist a set of \( n \) consecutive natural numbers such that the largest number in the set is a divisor of the least common multiple (LCM) of the remaining \( n - 1 \) numbers?
2. For which natural numbers \( n > 2 \) is there exactly one set that has the aforementioned property?

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