
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 the sum of positive numbers  $x_1, x_2, ... , x_n$  be  $1$ . 
Let  $s$  be the greatest of the numbers  $\big\{\frac{x_1}{1+x_1}, \frac{x_2}{1+x_1+x_2}, ..., \frac{x_n}{1+x_1+...+x_n}\big\}$ . 
What is the minimal possible  $s$ ? What  $x_i $ correspond it?

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