
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
 $A$  is a positive real number. $n$  is positive integer number.Find the set of possible values of the infinite sum  $x_0^n+x_1^n+x_2^n+...$  where  $x_0,x_1,x_2...$  are all positive real numbers so that the infinite series  $x_0+x_1+x_2+...$  has sum  $A$ .

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