\[\large{ \begin{cases} { \displaystyle \sum_{i=1}^{\infty} u_i = 3 } \\ { \displaystyle \sum_{i=1}^{\infty} u_i^2 = 3 } \end{cases}}\]

Let \(u_n\) be the \(n^{th}\) term of a geometric series satisfying the conditions above. Evaluate \(\lfloor 1000 u_{10} \rfloor \).

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