
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 the triplets of real numbers  $(x , y , z)$  such that : $y=\frac{x^3+12x}{3x^2+4}$  ,  $z=\frac{y^3+12y}{3y^2+4}$  ,  $x=\frac{z^3+12z}{3z^2+4}$ 

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