
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  $n>2$  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  $n>2$  is there exactly one set having this property?

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