Let $a$, $b$, $c$, and $d$ be positive real numbers such that $abcd=17$. Let $m$ be the minimum possible value of \[a^2 + b^2 + c^2 + a(b+c+d) + b(c+d) + cd.\] Compute $\lfloor 17m \rfloor$.

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