
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 equations:

$$
\begin{gathered}
6\left(x^{2} y^{2}+y^{2} z^{2}+z^{2} x^{2}\right)-49 x y z=0 \\
6 y\left(x^{2}-z^{2}\right)+5 x z=0 \\
2 z\left(x^{2}-y^{2}\right)-9 x y=0
\end{gathered}
$$

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