Let $x$, $y$, $z$ be positive real numbers satisfying the simultaneous equations
\begin{align*}x(y^2+yz+z^2)&=3y+10z\\y(z^2+zx+x^2)&=21z+24x\\z(x^2+xy+y^2)&=7x+28y.\end{align*}
Find $xy+yz+zx$.

Let's think step by step and output the final answer within \boxed{}.
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