
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  $(a,b,c)$  of real numbers all different from zero that satisfies: 

\begin{eqnarray}  a^4+b^2c^2=16a\nonumber  b^4+c^2a^2=16b \nonumber c^4+a^2b^2=16c \nonumber \end{eqnarray}


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