
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
$$
\left\{\begin{array}{r}
x_{1}+2 x_{2}+x_{3}=4 \\
3 x_{1}-5 x_{2}+3 x_{3}=1 \\
2 x_{1}+7 x_{2}-x_{3}=8
\end{array}\right.
$$
using Cramer's rule.

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