
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 $x_1, x_2, \ldots, x_{50}$ be positive real numbers such that $x_1^2 + x_2^2 + \ldots + x_{50}^2 = 1/2$. Find the minimum value of
\[
\sum_{i=1}^{50} \frac{x_i}{1 - x_i^2}.
\]

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