
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
There are 5000 boxes in a line. Each box $k$ (where $1 \le k \le 5000$) contains $3$ red marbles and $k^2$ white marbles. Maria begins at the first box and selects one marble at random from each box, moving in order. She stops when she draws a red marble for the first time. Let $Q(n)$ be the probability that Maria stops after drawing exactly $n$ marbles. Determine the smallest value of $n$ for which $Q(n) < \frac{1}{5000}$.
A) 122
B) 123
C) 124
D) 125

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