
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 in the set of real numbers, the system:  $$ x(3y^2+1)=y(y^2+3) $$    $$ y(3z^2+1)=z(z^2+3) $$    $$ z(3x^2+1)=x(x^2+3) $$  

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