
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
Given that \(x_{1}, x_{2}, \cdots, x_{n}\) are a set of positive numbers and their sum \(x_{1} + x_{2} + \cdots + x_{n} = c\), what values of \(x_{1}, x_{2}, \cdots, x_{n}\) will minimize the sum \(x_{1}^{\alpha} + x_{2}^{\alpha} + \cdots + x_{n}^{\alpha}\) where \(\alpha\) is a constant greater than 1?

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