
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 following system of four linear equations:

$$
\left\{\begin{aligned}
x + 7y + 3v + 5u & = 16 \\
8x + 4y + 6v + 2u & = -16 \\
2x + 6y + 4v + 8u & = 16 \\
5x + 3y + 7v + u & = -16
\end{aligned}\right.
$$

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