If $a, b, c, d$ are different digits from $1$ to $9$ such that $\frac{a}{b} + \frac{c}{d} \times 3 = N$, where $N$ is a whole number. What is the value of $\frac{c}{d} \times 3$ to maximize $N$? Let's think step by step and output the final answer within \boxed{}.
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