A circle with center \( C \) is tangent to the positive \( x \) and \( y \)-axes and externally tangent to the circle centered at \((3,0)\) with radius \( 1 \). Given that the center of the circle \( C \) is at \((r,r)\) where \( r \) is the radius of the circle, find the sum of all possible radii \( r \). Let's think step by step and output the final answer within \boxed{}.
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