
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 all triples  $ (x,y,z)$  of real numbers that satisfy the system of equations
\[ \begin{cases}x^3 \equal{} 3x\minus{}12y\plus{}50,  y^3 \equal{} 12y\plus{}3z\minus{}2,  z^3 \equal{} 27z \plus{} 27x. \end{cases}\]

*Razvan Gelca.*

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