
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 $y_1, y_2, y_3, \ldots, y_{50}$ be positive real numbers such that $y_1^2 + y_2^2 + y_3^2 + \ldots + y_{50}^2 = 1$. Find the minimum value of
\[
\frac{y_1}{1 - y_1^2} + \frac{y_2}{1 - y_2^2} + \frac{y_3}{1 - y_3^2} + \ldots + \frac{y_{50}}{1 - y_{50}^2}.
\]

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