
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:

\[
\begin{cases}
x_{1} + 2 x_{2} + 2 x_{3} + 2 x_{4} + 2 x_{5} = 1 \\
x_{1} + 3 x_{2} + 4 x_{3} + 4 x_{4} + 4 x_{5} = 2 \\
x_{1} + 3 x_{2} + 5 x_{3} + 6 x_{4} + 6 x_{5} = 3 \\
x_{1} + 3 x_{2} + 5 x_{3} + 7 x_{4} + 8 x_{5} = 4 \\
x_{1} + 3 x_{2} + 5 x_{3} + 7 x_{4} + 9 x_{5} = 5
\end{cases}
\]

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