We start with the point \((1,3)\) of the plane. We generate a sequence of points with the following rule: the \(x\)-coordinate of the new point is the arithmetic mean of the \(x\) and \(y\) coordinates of the previous point, and the \(y\)-coordinate of the new point is the harmonic mean of the \(x\) and \(y\) coordinates of the previous points. The harmonic mean of two numbers \(x\) and \(y\) is \(\frac{2}{\frac{1}{x} + \frac{1}{y}}\). Is the point \((3,2)\) in the sequence?