Find the largest four-digit number that is divisible by 7 and is written with four different digits.

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Let's sequentially select the largest possible values for the thousands, hundreds, and tens digits, that is, we will look for a number of the form $\overline{987 A}$. The number 987 is divisible by 7, so $A$ must also be divisible by 7. Since the value $A=7$ cannot be chosen, then $A=0$.

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