Can I request for some action shots from this lens? It doesn't have to be fast sports or anything similar, I would just like to see if its possible to shoot moving subjects with this relatively-slow AF'ing lens.
Moving subjects? How about a bird in flight? (full image and 100% crop)

EOS 7D, EF 85mm f/1.2
L II, 1/1600 s, f/6.3, ISO 2000
Still, the grackle was pretty far away - the 85L doesn't do very well with close, erratically-moving subjects, even if they're not moving too fast. The body you use makes a difference, too. The 7D will track moving subjects better than the 5DII, even with a comparitively slow lens like the 85L. A 1-series body would do even better.