A right circular cone has a base with radius that is equal to the arithmetic average of the cone's height and generatrix. Given that the volume of the cone is **128π m³**, what is the value, in meters, of the base's radius and the height of the cone, respectively?

**Note**: this problem was not created by me. It is from the Technological Institute of Aeronautics (in Portuguese, *Instituto Tecnológico de Aeronáutica*, **ITA**).

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