
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
Given that each of 3000 boxes contains a single red marble and, for $1 \le k \le 3000$, the box in the kth position contains k^2 white marbles, calculate the smallest value of n for which the probability that Isabella stops after drawing exactly n marbles is less than 1/3000.

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