
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

Given the numbers \(x_{1}, x_{2}, x_{3}, \ldots, x_{2018}\). It is known that \(x_{1}= \frac{1}{2}\) and 

$$
x_{n}=\frac{x_{n-1}}{2 n x_{n-1}+1} \text { for } n=2, \ldots, 2018
$$

Find the sum \(x_{1}+x_{2}+\cdots+x_{2018}\).

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