I've puréed sweet potatoes before as a result of advice from the book "Deceptively Delicious." I found the easiest way to make a sweet potato purée was to bake the potatoes, skin them, mash them and out them in a blender or stand mixer with some water or other liquid. I don't have a decent food processor. Having one of those would have probably made the whole process easier.

A mashed sweet potato recipe would probably be a decent start.

As for the strawberries, you might find it easier to buy strawberry puree or juice. The Mexican or "ethnic" food aisle in the local grocery should have the juice and the puree can often be found in sweetened form in the baking aisle as a pie filling.

You can also get cans of coked sweet potatoes.