
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 sequence of $4020$ boxes, each box contains one red marble. Additionally, for $1 \leq k \leq 4020$, the box in the $k\text{th}$ position contains $k^2$ white marbles. Eliza begins at the first box and draws a single marble at random from each box, sequentially. She stops when she first draws a red marble. Let $Q(n)$ be the probability that Eliza stops after drawing exactly $n$ marbles. What is the smallest value of $n$ for which $Q(n) < \frac{1}{4020}$?
A) 62
B) 63
C) 64
D) 65
E) 66

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