Given that $a_{i} \in \{0,1,2,3,4\}$ for every $0 \le i \le 9$, if $6\sum_{i=0}^{9}a_{i} 5^{i} \equiv 1 \pmod{5^{10}}$, find the value of $a_{9}$.

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