
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
Divide the sequence of positive integers \(1, 2, \cdots\) in such a way that the first segment contains \(1 \times 2\) numbers, the second segment contains \(2 \times 3\) numbers, ..., the \(n\)-th segment contains \(n \times (n+1)\) numbers. Determine which segment contains the number 2014.

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