
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
In a math class, the teacher wrote a number on the board. One student said, "The number is divisible by 31." The second student said, "The number is also divisible by 30." A third student claimed the number is divisible by 29, a fourth said it is divisible by 28, and so on, until the thirtieth student stated that the number is divisible by 2.

The teacher then revealed that out of the thirty statements, only two were false, and these two false statements were made consecutively.

Which were the two false statements?

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