
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 were discussing a large positive integer. Each friend speculated that this number could be divided by consecutive integers from 1 up to 30. ``It can be divided by 1,'' stated the first friend. ``It can be divided by 2,'' added the second friend, and so on until the last (30th) friend remarked, ``It can be divided by 30.'' If exactly two friends were incorrect with their statements and those two friends said consecutive numbers, find the least possible integer they might have been discussing.

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