I'm having problems when trying to know the outcome of this reaction.

The first step must be a Michael addition of the 1,3-dicarbonyl compound to the α,β-unsaturated carbonyl compound, followed by a acid hydrolisis and a decarboxylation of the ester.

LDA must deprotone the least hindered hydrogen, that must be the $\alpha$-$\ce{CH3}$ to the non cyclic ketone. But at this point, I don't know how this reaction can continue to give one of the above products.