
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
Let $N$ be a positive multiple of $8$. Two red balls and $N$ green balls are arranged in a row in random order. Let $Q(N)$ be the probability that at least $\tfrac{3}{4}$ of the green balls are on the same side of either of the red balls. Assume that $Q(8)=1$ and that $Q(N)$ approaches $\tfrac{7}{8}$ as $N$ increases. Find the sum of the digits of the least value of $N$ such that $Q(N) < \tfrac{319}{400}$.
A) 7
B) 8
C) 9
D) 10

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