Sorting a list of articles by logged-in user


How it is possible for the logged-in user to choose how sort a list of products (by relevance, price or date) ?
The dropdownmenu doesn’t allow to create an action. If the dropdown menu is turned into a list, it allows action but doesn’t seem to take the selected item into account.
Anyway, I didn’t find a way for the action to update the way of sorting a list. Do I need to create a custom action ?

Thanks a lot for your help