Anyone else here having problems using canes in restaurants that have tile floors?

I went into an Arby's tonight. It was raining. The employees had taken up the rugs in the entryway (that was full of water because there was no awning over the door and the rain was coming into the doorway every time someone opened the door. (oh, and no handy "Wet Floor" sign anywhere in sight to warn people that the floor might be wet)

So, there was an inch of standing water in that doorway. I had to hang onto the wall to get inside to avoid slipping. Get inside, and they'd taken up the rugs in there too so they could mop in there. I couldn't use my cane on the floor in there either.

When we were leaving, I thought the floor would finally be dry, put my cane down, tested the weight a little bit, and just about killed myself when the cane slid away from me. My dad also uses a cane, and he really uses it to hold himself up, so he was having a harder time than I was walking across that floor.

Anyone know how to walk on slick, wet tile floors with a cane without killing themselves?