How do cell membranes and the cytoskeleton assist each other by working together?
Well, the cell membrane and cytoskeleton are both cellular organelles. The cell membrane helps regulate or control what enters and leaves the cell. The cytoskeleton helps in cellular support and movement of substances within the cell. So, the biggest connecting point between the two is movement of substances. The cell membrane allows the substances in and the cytoskeleton helps the substance move once it is inside the cell. The same is true of the reverse. The cytoskeleton can help move substances that are inside the cell towards the cell membrane. Once at the cell membrane, the substance can exit the cell.
The cytoskeleton works as a framework for the cell- helps to keep the shape of the cell. And in return, the cell membrane helps the cytoskeleton to attach to the innard of the cell.
I think cytoskeleton filaments (particles) stick to the carbohydrates sticking out of the cell membrane. I'm not sure about that. But I'm sure that the cell membrane helps cytoskeleton to be IN the cell.