### Initialization 

The algorithm begins by **randomly** selecting **K** initial cluster centers, also known as **centroids**. These centroids serve as the starting points for each cluster. A common approach is to randomly choose K data points from the dataset to be the **initial centroids**.

### Assignment Step 

In this step, each data point is assigned to the **closest centroid**. The distance is typically measured using **Euclidean distance**, but other distance metrics can also be used. Each data point is placed into the cluster represented by the nearest centroid.

### Update Step 

Once all data points are assigned to clusters, the centroids are **recalculated**. For each cluster, the new centroid is computed as the **mean of all the data points belonging to that cluster**. Essentially, the centroid is moved to the center of its cluster. 

### Iteration

Steps 2 and 3 are repeated iteratively. In each iteration, data points are **reassigned to clusters** based on the updated centroids, and then **centroids are recalculated** based on the new cluster assignments. This iterative process continues until a stopping criterion is met.  

### Convergence 

The algorithm stops when one of the following conditions is met: 

- **Centroids do not change significantly:** the positions of the centroids stabilize, meaning that in subsequent iterations, there is minimal change in their locations; 

- **Data point assignments do not change:** data points remain in the same clusters, indicating that the cluster structure has become stable; 

- **Maximum number of iterations is reached:** a pre-defined maximum number of iterations is reached. This prevents the algorithm from running indefinitely. 

Upon convergence, the K-means algorithm has partitioned the data into **K clusters**, with each cluster represented by its centroid. The resulting clusters aim to be **internally cohesive** and **externally separated** based on the chosen distance metric and the iterative refinement process. 

During the update step in the K-means algorithm, what is the main action performed?

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