
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
A series of 2500 boxes are aligned in a row, each box containing a definitive single red marble and an ascending count of white marbles equal to its position number (i.e., the $k$th box contains $k$ white marbles). Additionally, if a box number is divisible by 5, it contains one extra green marble. Isabella picks a marble randomly from each box, starting from the first box, and stops as soon as she picks a green marble. Let $Q(n)$ denote the probability that Isabella stops after exactly picking $n$ marbles. Determine the smallest $n$ for which $Q(n) < \frac{1}{2500}$.
A) 15  
B) 17  
C) 19  
D) 20  
E) 21

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