
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 club of 30 friends was reviewing a large positive integer. Starting with the first friend, who said, "It can be divided by 1," each subsequent friend added that the number could be divided by the next integer in sequence (2, 3, 4, etc.) until all 30 friends had spoken. However, exactly two of the friends, and not necessarily the last two, had spoken incorrectly, and these incorrect claims involved two consecutive numbers. What is the least possible integer they could have been discussing if the two incorrect consecutive numbers were as high up in the sequence as possible?

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