
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
Find the general solution of the nonhomogeneous system

$$
\left\{\begin{array}{l}
x_{1} + 7 x_{2} - 8 x_{3} + 9 x_{4} = 1 \\
2 x_{1} - 3 x_{2} + 3 x_{3} - 2 x_{4} = 1 \\
4 x_{1} + 11 x_{2} - 13 x_{3} + 16 x_{4} = 3 \\
7 x_{1} - 2 x_{2} + x_{3} + 3 x_{4} = 4
\end{array}\right.
$$

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