
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

\[
\left\{
\begin{aligned}
x_{1} + 2x_{2} - x_{3} + x_{4} - 2x_{5} &= -3 \\
x_{1} + 2x_{2} + 3x_{3} - x_{4} + 2x_{5} &= 17 \\
2x_{1} + 4x_{2} + 2x_{3} &= 14
\end{aligned}
\right.
\]

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