Suppose the function $f(x,y,z)=xyz$ is defined for $x+y+z=7$, $x,y,z \ge 0$. What is the range of $f$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Suppose the function $f(x,y,z)=xyz$ is defined for $x+y+z=7$, $x,y,z \ge 0$. What is the range of $f$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\left[0,\frac{343}{27}\right]
Suppose the function $f(x,y,z)=xyz$ is defined for $x+y+z=7$, $x,y,z \ge 0$. What is the range of $f$?
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