
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 sequence of  $N$  consecutive positive integers is called *good* if it is possible to choose two of these numbers so that their product is divisible by the sum of the other  $N-2$  numbers. For which  $N$  do there exist infinitely many *good* sequences?

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