…Keep in mind each step can only include the addition of molecules with two or three carbons.
This is the most important comment. What chemistry was being discussed in class if we are going to guess the appropriate chemistry?
I could imagine a double Mannich with acetone, formaldehdye, and benzylamine to give the piperidinone. If cyanide were added to the imine from the ketone and allylamine, base hydrolysis to the amide, and cyclization with formaldehyde would give the product. Obviously, if Diels-Alder reactions are being discussed in class, this would be going in the wrong direction. My route is all about carbonyl chemistry.