In a clustering problem, the input data set contains the following five data points (1,2), (2,2), (4,4), (5,4), (5,5). The k-means clustering method is used to find two clusters (k=2). The Manhattan distance is chosen to compute the distance between two data points, and the initial centroids are (1,2) and (2,2).
Describe the steps of the k-means clustering. (In each step, provide the information about the cluster assignments of data points, centroids, and when the algorithm stops).