More Walking Problems

This morning I reached the elevator in the parking deck at nearly the same time as a middle-aged woman, whom I do not know. When the elevator arrived, I let her enter first, according to the principle of “ladies first.” After doing so, however, I had second thoughts. Would this woman feel uncomfortable having a young man walk behind her into a sealed box? When the doors opened I faced the same problem, but once again came to the same decision. It seemed rude to exit first, so I let her go ahead. Of course, this had the domino effect of making her the first person to reach the door to exit the building. At this point I was hoping she would stand at the door and hold it in order to let me go ahead, but unfortunately she merely held the door behind her, so that I remained behind. I would have liked to walk quickly ahead to be able to open the next door for her, but doing so surely would have seemed strange and perhaps threatening. So once again the young man had the door opened for him by the middle aged woman. It seemed so backwards, but there was nothing I could do. We finally reached the elevator inside the office building together, and shared a short, but still awkward ride several floors up.

What should I have done????