
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 warehouse, there are 2023 boxes arranged in a row. Each box contains a green marble, and for $1 \leq k \leq 2023$, the box at the $k\text{th}$ position contains an additional $2k$ blue marbles. Jenny begins at the first box and randomly picks a single marble from each box, moving sequentially. She stops when she first draws a green marble. Let $Q(n)$ be the probability that Jenny stops after drawing exactly $n$ marbles. What is the smallest value of $n$ for which $Q(n) < \frac{1}{2023}$?
A) 31
B) 32
C) 33
D) 34
E) 35

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