
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
Determine all real solutions  $x, y, z$  of the following system of equations:  $\begin{cases}
x^3 - 3x = 4 - y 
2y^3 - 6y = 6 - z 
3z^3 - 9z = 8 - x\end{cases}$ 

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