While the order of then and next in a list is very fluid (IMO there's no strict rule as to which goes first), next does usually have to be used in a formal list such as a list of instructions. For example:
She inspected me with her eyes. Next, she brought a tiny hand to her chin and said, "I think I know you." Finally, she closed the eyes that had previously being inspecting me.
Despite there bring three actions, this sounds unnatural because it is prose, but words like next and finally belong in a list of instructions or similar.
She inspected me with her eyes. Then, she brought a tiny hand to her chin and said, "I think I know you." before closing the eyes that previously been inspecting me.
This sounds much more natural because words like then and before were used (which fit better into prose).
Note that next and before (and and) can still be used in formal lists, but not the other way around.