
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:

\[
\left\{\begin{aligned}
x_{1}-2 x_{2}+3 x_{3} &= 5 \\
2 x_{1}+3 x_{2}-x_{3} &= 7 \\
3 x_{1}+x_{2}+2 x_{3} &= 12
\end{aligned}\right.
\]

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