
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:

$$
\begin{aligned}
& \left(x_{3}+x_{4}+x_{5}\right)^{5}=3 x_{1}, \\
& \left(x_{4}+x_{5}+x_{1}\right)^{5}=3 x_{2}, \\
& \left(x_{5}+x_{1}+x_{2}\right)^{5}=3 x_{3}, \\
& \left(x_{1}+x_{2}+x_{3}\right)^{5}=3 x_{4}, \\
& \left(x_{2}+x_{3}+x_{4}\right)^{5}=3 x_{5}.
\end{aligned}
$$

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