
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:

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

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