
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) For which values of \( n > 2 \) is there a set of \( n \) consecutive positive integers such that the largest number in the set is a divisor of the least common multiple of the remaining \( n-1 \) numbers?

(b) For which values of \( n > 2 \) is there a unique set having the stated property?

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