[Mockito] Mocking void methods to set a passed in parameter

Consider the following badly designed code:
 

public interface BadPrecedentService {
    void setThePassedInList(List items);
}

This is being used as below:

public class BadPrecedentClient {
    private final BadPrecedentService badPrecedentService;
    public BadPrecedentClient(BadPrecedentService badPrecedentService) {
	this.badPrecedentService = badPrecedentService;
    }
    public List getNamesOfActiveItems() {
	List items = new ArrayList(10);
	badPrecedentService.setThePassedInList(items);
	List names = new ArrayList(items.size());
	for (Item item : items) {
	    if (item.isActive()) {
		names.add(item.getName());
	    }
	}
	return names;
    }
}

How can I test this method with Mockito? Look at the following snippet:

public class BadPrecedentClientTest {
    @Test
    public void testGetNamesOfActiveItems() {
	// given
	BadPrecedentService badPrecedentService = mock(BadPrecedentService.class);
	doAnswer(new Answer