
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 \(x_1, x_2, x_3, x_4, x_5\) be positive real numbers such that \(x_1^3 + x_2^3 + x_3^3 + x_4^3 + x_5^3 = 1.\) Find the minimum value of
\[
\frac{x_1}{1 - x_1^2} + \frac{x_2}{1 - x_2^2} + \frac{x_3}{1 - x_3^2} + \frac{x_4}{1 - x_4^2} + \frac{x_5}{1 - x_5^2}.
\]

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