\[\begin{cases}a+2b+3c &=&1\\a^2+b^2+c^2 &=&29 \end{cases}\]

Suppose \(a,b\) and \(c\) are real numbers fulfilling the above equations. Find the minimum value of \(\lfloor 1000c\rfloor\).

**Notation**: \( \lfloor \cdot \rfloor \) denotes the floor function.

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