
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  $ \begin{cases} x^3 \plus{} x(y \minus{} z)^2 \equal{} 2 y^3 \plus{} y(z \minus{} x)^2 \equal{} 30 z^3 \plus{} z(x \minus{} y)^2 \equal{} 16\end{cases}$ .

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