
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
For any \( n \in \mathbf{N}^{*} \) and \( a \in \mathbf{R} \), solve the system of equations
$$
\left\{\begin{array}{l}
x_{1}+x_{2}+\cdots+x_{n}=a, \\
x_{1}^{2}+x_{2}^{2}+\cdots+x_{n}^{2}=a^{2}, \\
\cdots \cdots \\
x_{1}^{n}+x_{2}^{n}+\cdots+x_{n}^{n}=a^{n}.
\end{array}\right.
$$

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