Anna and Bob are participating in a relay race where each person runs a certain distance. Anna runs $3$ miles $1200$ yards, and Bob runs $5$ miles $800$ yards. One mile equals $1760$ yards. If the total distance run by Anna and Bob is $m$ miles and $y$ yards, where $0 \le y < 1760$, what is the value of $y$? Let's think step by step and output the final answer within \boxed{}.
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