
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
If the product of three consecutive integers is divided by their sum, the quotient is 5. What are these numbers?

In general: when will the quotient obtained in the aforementioned manner be an integer? For instance, which group of numbers will directly follow the group identified in the previous part in magnitude?

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