
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 following system of equations:

$$
\begin{aligned}
& x_{1}+2 x_{2}+3 x_{3}+\ldots+9 x_{9}+10 x_{10}=55, \\
& x_{2}+2 x_{3}+3 x_{4}+\ldots+9 x_{10}+10 x_{1}=55, \\
& \vdots \\
& x_{10}+2 x_{1}+3 x_{2}+\ldots+9 x_{8}+10 x_{9}=55 .
\end{aligned}
$$

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