Let $f(x) =x^4+14x^3+52x^2+56x+16.$  Let $z_1, z_2, z_3, z_4$ be the four roots of $f$.  Find the smallest possible value of $|z_az_b+z_cz_d|$ where $\{a,b,c,d\}=\{1,2,3,4\}$.

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