The carousel is now showing its first child item but there's no way to change what's displayed. It needs a selected property to control which item is shown.
Add the selected property accessor and accompanying code above the render method.
The user can set selected to any value, but it's only a valid selection if it's a number in the range of the total number of items in the carousel. The selectedInternal private property is clamped to this valid range and will be used in a later step.