Cunning Maximum

Algebra Level 4

\[ \frac{ (ab)^2 + (bc)^2 + (ca)^2 + 12abc + 72}{ab+bc+ca} - \frac{abc}2 \]

If \(1 \leq a,b,c \leq 3 \) such that \(a+b+c=6\), find the maximum value of the expression above.

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