Adam was reminiscing the memories he's got with Hana when they were still in the Cerulean Kingdom. True, he's got a hard time there because he would be punished every time they would sneak out of the palace but those stolen moments were very precious to him as well. He loved those moments the best.
However, everything must come to and end and to him, that ending happened when Jacob came into their lives. At the same time, he couldn't blame anyone. If you're destined to be together, you will still be together in the end. The happy ending for Hana might not be in this lifetime but, he knew it will come for sure.
Adam walked aimlessly, he wanted to be away from them, away from the source of his jealousy and pain. He found a nearby park and stayed there without any purpose. He watched the children play their kind of games and watched the parents chat. There were couples who strolled around and there were singles like them, too.