Help with AE: does anyone know how to animate paths imported from Illustrator?

As shown in the very basic example below — I have a green path that I want to keyframe the blue circle along; both were made and imported from Illustrator. That’s the first step.

The second challenge is to then create a blur mask via adjustment layer, wherein the blur mask in the adjustment layer is pick-whipped to the blue circle’s path shape, such that a blur that is the exact same dimensions as the blue circle animates along the green path and blurs the faint checkered background.

Any suggestions on how to achieve this? Thank you all for your time.