Let m: [0,1) -> [0,1) be the function defined by m(x) = 2x(mod 1). Find all points in [0,1) that satisfy m^4(x) = x. Note that this will contain the period four points, but others as well. Express your answer as a rational number using decimal digits, e.g., 1/3. Organize the points into their respective cycles. (This problem can be solved using the geometric series formula only once, so try to be clever in solving it to save a lot of work.)