
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, starting with the first, said the integer can be divided by an incremental number: "It can be divided by 1," said the first friend; "It can be divided by 2," said the second friend, and so on up to 30. However, exactly three friends made incorrect statements with their numbers being consecutive. Identify the least possible integer they were discussing if friends' incorrect statements were 27, 28, and 29.

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