
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
If  $x_{1}, x_{2},\ldots ,x_{n}$  are positive real numbers with  $x_{1}^2+x_2^{2}+\ldots +x_{n}^{2}=1$ , ﬁnd the minimum value of  $\sum_{i=1}^{n}\frac{x_{i}^{5}}{x_{1}+x_{2}+\ldots +x_{n}-x_{i}}$ .

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