
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 positive integer. Solve the system of equations \begin{align*}x_{1}+2x_{2}+\cdots+nx_{n}&= \frac{n(n+1)}{2} x_{1}+x_{2}^{2}+\cdots+x_{n}^{n}&= n\end{align*} for  $n$ -tuples  $(x_{1},x_{2},\ldots,x_{n})$  of nonnegative real numbers.

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