
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
Given the real numbers \(x_{1}, x_{2}, x_{3}, x_{4}, x_{5}\) satisfy the system of equations:
\[
\begin{cases}
x_{1}+x_{2}+x_{3}=a_{1} \\
x_{2}+x_{3}+x_{4}=a_{2} \\
x_{3}+x_{4}+x_{5}=a_{3} \\
x_{4}+x_{5}+x_{1}=a_{4} \\
x_{5}+x_{1}+x_{2}=a_{5}
\end{cases}
\]
where \(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\) are real constants and \(a_{1}>a_{2}>a_{3}>a_{4}>a_{5}\), determine the order of \(x_{1}, x_{2}, x_{3}, x_{4}, x_{5}\).

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