
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 members discusses a large positive integer. Each member claims divisibility of this integer by consecutive integers starting from 1. "It is divisible by 1," says the first member. The second member confirms divisibility by 2, and so on up to divisibility by 30. However, exactly three members, claiming consecutively, are wrong about their assertions. What is the smallest possible integer they could be discussing?

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