Find the minimum of $x + y + z$ where $x$, $y$, and $z$ are real numbers satisfying the following conditions:
- $x \geq 4$
- $y \geq 5$
- $z \geq 6$
- $x^2 + y^2 + z^2 \geq 90$

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