
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 solution to the system:

$$
\left\{\begin{array}{l}
5 x^{7}+3 y^{2}+5 u+4 v^{4}=-2 \\
2 x^{7}+8 y^{2}+7 u+4 v^{4}=\frac{6^{5}}{3^{4} \cdot 4^{2}} \\
8 x^{7}+2 y^{2}+3 u+6 v^{4}=-6 \\
5 x^{7}+7 y^{2}+7 u+8 v^{4}=\frac{8^{3}}{2^{6} \cdot 4}
\end{array}\right.
$$

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