
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

$$
\left\{\begin{aligned}
x_{1}+x_{3}+2 x_{4}+3 x_{5}-4 x_{6}= & 20 \\
2 x_{1}+x_{2}-3 x_{3}+x_{5}+2 x_{6}= & -13 \\
5 x_{1}-x_{2}+x_{3}+2 x_{4}+6 x_{5} & =20 \\
2 x_{1}-2 x_{2}+3 x_{3}+2 x_{5}+2 x_{6} & =13
\end{aligned}\right.
$$

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