ipad_Lover, you might wish to give Contrast a try, it is on both PS3 and PS4.
They categorise it as action, puzzle, unique, and I saw platformer as well. But really it is simply unique.
Frankly I feel this is just an adventure without any stress and not much in the way to classify it as action or more puzzle oriented than most adventures. It is the closest to an adventure I have found so far on PS4, despite sometimes difficult manoeuvres jumping over shadows on the walls. So there are action bits.
It has a wonderful feel of old Paris or Montréal in 1923 with jazz or soul music and a great plot of a little girl wanting to get her parents back together (although this is not her real father). All in an ghostly atmosphere of cabaret, circus and shadows. It is a bit like the feel you find in the animated film A Cat in Paris.
This is the best adventure I have played in a long time, like you can only experience it on PS4, and it is only 12.79 in the UK, quite affordable.
Really worth it, and nothing as complicated as those demons in Murdered Soul Suspect, which had me leave the game alone for days. I am almost afraid of trying that game again. I won't even talk about Watch Dogs, I played it for five minutes so far. However to be fair I just have no time at the moment to give them a real chance.
For Contrast though I have all the time in the world. I could feel already how I slept better just thinking about and being enrobed in the beautiful atmosphere they built in there. It gives me a real sense of evasion from reality. Five stars.