
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 linear equations using the Gaussian elimination method.

$$
\begin{aligned}
& 2 x_{1}+7 x_{2}+13 x_{3}=0 \\
& 3 x_{1}+14 x_{2}+12 x_{3}=18 \\
& 5 x_{1}+25 x_{2}+16 x_{3}=39
\end{aligned}
$$

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