Smallest area of triangle

Geometry Level 4

As shown in the figure, given two fixed points, \(O=(0,0)\) and \(A=(10,10)\). \(C\) is a point on \(x\)-axis, while \(D\) is a point on a straight line, which make a \(60^\circ\) with \(x\)-axis. Now the three points \(C, A\) and \(D\) lie on a straight line.

Let the smallest possible value of the area of triangle \(OCD\) be \(s\). Find the value of \(\lfloor 1000s\rfloor\).

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