
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
The sequence \(a_{1}, a_{2}, \ldots\) consists of positive numbers and its limit is 0. What is the limit of the following sequence?

$$
b_{n}=\frac{1}{n}\left(\frac{a_{1}}{1+a_{1}}+\ldots+\frac{a_{n}}{1+a_{n}}\right)
$$

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