
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 in the set of real numbers:

$$
\left.\begin{array}{l}
y^{3}-6 x^{2}+12 x-8=0 \\
z^{3}-6 y^{2}+12 y-8=0 \\
x^{3}-6 z^{2}+12 z-8=0
\end{array}\right\}
$$

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