
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
For $i = 2, 3, \ldots, k$, the remainder of a positive integer $n$ divided by $i$ is $i - 1$. If the minimum value of $n$, denoted as $n_0$, satisfies $2000 < n_0 < 3000$, then the minimum value of the positive integer $k$ is.

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