
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 circle of 17 friends were sharing thoughts about a large positive integer. Each friend declared, "It can be divided by the $n^\text{th}$ prime number," corresponding to their turn in the circle. If exactly two friends were incorrect, and these friends said consecutive primes, what was the smallest possible integer they were discussing, assuming it is divisible by 1?

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