
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 there be $k$ red balls and $N$ green balls arranged in a line, where $k$ is a positive integer and $N$ is a positive multiple of 10. Determine the least value of $N$ such that the probability that at least $\frac{3}{5}$ of the green balls are on the same side of all the red balls combined is less than $\frac{8}{10}$ when there are $2$ red balls, and calculate the sum of its digits.

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