
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
Solve the system of equations
\[
\begin{cases}
x_{1} + x_{2} + \cdots + x_{n} = n \\
x_{1}^{2} + x_{2}^{2} + \cdots + x_{n}^{2} = n \\
\cdots \\
x_{1}^{n} + x_{2}^{n} + \cdots + x_{n}^{n} = n
\end{cases}
\]

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