
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  $n$  be a nonzero natural number, and  $x_1, x_2,..., x_n$  positive real numbers that  $ \frac{1}{x_1}+\frac{1}{x_2}+...+\frac{1}{x_n}= n$ . Find the minimum value of the expression  $x_1 +\frac{x_2^2}{2}++\frac{x_3^3}{3}+...++\frac{x_n^n}{n}$ .

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