
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 linear system

$$
\left\{\begin{aligned}
-x_{1}-2 x_{2}-6 x_{3}+3 x_{4} & =-1 \\
2 x_{1}+5 x_{2}+14 x_{3}-7 x_{4} & =3 \\
3 x_{1}+7 x_{2}+20 x_{3}-10 x_{4} & =4 \\
-x_{2}-2 x_{3}+x_{4} & =-1
\end{aligned}\right.
$$

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