An exercise day is considered a day with a workout. A "workout" is considered an auto-recognized activity continued for at least the minimum amount of time. Note the minimum time I believe is set at 15 minutes bet can be adjusted between 10 and 90 minutes. If you don't trust your activity will be auto-recognized, anything you do using the Exercise App will also be called a workout. I have not verified this, but I expect that means it would also make it count as an "exercise day".
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