While I’d like to imagine that Trump was intellectually coherent enough to be repaying his debt to Putin I suspect the real answer is simply that he’s an infantile moron who is so deeply inadequate that he unconsciously believes he can gain strength by cozying up to bullies and thugs. In this modality a suggestion by Putin can become, in what passes for Trump’s tiny mind, a “smart and stable genius” idea that he rushes to implement so he can show the world how “strong and genius” he is.
As Trump knows nothing and understands nothing, he’s eminently manipulable. As NK’s pocket-sized dictator has shown multiple times, as Putin has shown many times, and no doubt every other cynical dictator will show over the years ahead (because, sadly, Trump supporters are as ignorant and foolish as their Great Orange Leader and so he’ll win re-election in 2020).