A list of numbers [5, 2, 8, 1, 9, 4] needs to be sorted using the merge sort algorithm. Explain how the merge sort algorithm works by describing the 'divide' and 'conquer' (merge) steps for this list.

Merge sort is a classic sorting algorithm that exemplifies the "divide and conquer" paradigm. **1. The Divide Step:** The main list is treated as a problem to be solved. The algorithm's first step is to break this problem into smaller, more manageable sub-problems. It does this by splitting the list in half. It then takes each of those halves and splits them in half again. This process continues recursively until the lists cannot be split any further, which is when they each contain only one element. A list with one element is, by definition, already sorted. **2. The Conquer (Merge) Step:** Once the list is broken down into single-element sub-lists, the algorithm begins to "conquer" by merging them back together. When two sub-lists are merged, a new sorted list is created by comparing the elements from the two lists one by one and adding the smaller one to the new list. This ensures the newly created list is sorted. This merging process is repeated up the hierarchy until all the sub-lists have been merged back into a single list, which is now fully sorted.