I thought you might like to know how the dog training works. Your character replaces the dog trainer when you click on him and train your dog. Your dog replaces the one running around the course. That's it. Here is a photo of me training Purincess.

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Here is the prize when you finish training your doggie. (I put it in a spoiler in case you want to be suprised) I trained my dog for 3 days before receiving it.

Spoiler: