The last time Dumbledore can remember the Elder wand in his possession he was having a peaceful break at the blue table bench you are at now. He cannot remember where exactly he went after, but he can vaguely remember walking towards the heart of Hogwarts (UB South), as well as walking up steps very shortly after ending his break at the blue table. For some reason Dumbledore keeps referring to the steps as platforms. And you make note that he tends to hug the right railing.
ps, you can take the labels off as you go!!
Kings cross station = Staircase
Platforms = Steps
Bottom railing right side