
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 sequence contains one red ball, one blue ball, and $N$ green balls where $N$ is a positive multiple of 7. Calculate the probability $P(N)$ such that at least $\frac{2}{3}$ of the green balls are on the same side as the red ball but on the opposite side of the blue ball. Determine the least value of $N$ for which $P(N) < \frac{7}{10}$, and find the sum of its digits.

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