Which death note did the task force have?

So as far as I am aware, there are/was 4 death notes in the human world. Lights (which was gegeven back to the shimigani), misa's (which was jealous's) Rem's (after he died) and riuk's.

During the series the task force gets one of the notebooks (lights) and then Rem kills L leaving his personal one in human world. So is that two in the tasks forces possession?

Later on, lights death note is traded for his sister and mello has it but it is then returned to the chocolate eating shimigani. Then further on in the series Near asks to use the death note to kill Mello to see if the 13 dag rule is a fake so my main vraag is, who's death note was he asking to use? Did the task force still have one (Rem's) in their possession and if not why was riuk still with the task force and if not, where was Rem's death note at this point?