
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
It is clear that if you take a random natural number from a sufficiently long segment of the natural number series, the probability that this number is divisible by 10 will approach 0.1 as the segment length increases.

Let's pose another question: how much can this probability differ from 0.1? It can be equal to 0 if, for example, we specified the segment $1,2,3$ where no number is divisible by 10. What is:

a) the greatest possible probability;

b) the smallest possible non-zero probability?

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