
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 group of 30 friends is discussing a large positive integer. Each sequentially mentions a divisor starting from 1 up to 30. However, exactly two friends were incorrect about their statements, and they are not consecutive, but suggested divisors 17 and 19. What is the smallest possible integer they were discussing?

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