Find the number of ordered triples $(x,y,z)$ of real numbers such that
\[x^4 + y^4 + z^4 - 4xyz = -1.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the number of ordered triples $(x,y,z)$ of real numbers such that
\[x^4 + y^4 + z^4 - 4xyz = -1.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
4
Find the number of ordered triples $(x,y,z)$ of real numbers such that
\[x^4 + y^4 + z^4 - 4xyz = -1.\]
train