
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 $3$. One blue ball and $N$ yellow balls are placed in a line in a random order. Define $P(N)$ as the probability that at least $\tfrac{2}{3}$ of the yellow balls are on one side of the blue ball. Determine $P(N)$ for the smallest $N$ such that $P(N) < \tfrac{3}{4}$. What is the sum of the digits of this $N$?
A) 5
B) 6
C) 7
D) 8
E) 9

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