In this addition problem, each letter stands for a different digit.
$$\begin{array}{cccc}&T&W&O\\+&T&W&O\\\hline F&O&U&R\end{array}$$
If $T = 7$ and the letter $O$ represents an even number, what is the only possible value for $W$?

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