\(a, b\) and \(c\) are positive real numbers greater than or equal to 1 satisfying

\[ \begin{align} abc & =100,\\ a^{\lg a} b^{\lg b} c^{\lg c} & \geq 10000. \\ \end{align} \]

What is the value of \(a + b + c \)?

**Details and assumptions**:

- \(\lg\) refers to log base 10.

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