
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
 $\boxed{A1}$  Find all ordered triplets of  $(x,y,z)$  real numbers that satisfy the following system of equation  $x^3=\frac{z}{y}-\frac {2y}{z}$   $y^3=\frac{x}{z}-\frac{2z}{x}$   $z^3=\frac{y}{x}-\frac{2x}{y}$ 

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