My grandson Dorian is now just past three, and he has very recently achieved two major cognitive milestones.
On the one hand, he now can say that the person he sees in the mirror or the looped-back video camera is himself. I saw him just yesterday standing in front of a full-length mirror on the floor and saying "A picture of Dorian!" On the other hand, he now will come up to an adult and say "You need to change my diaper!" when he has pooped in it. Both of these are very significant advances over just a month ago.
Until now, Dorian could pass the mirror test (like humans and other great apes, dolphins, killer whales, and magpies) in the sense that he showed recognition of himself in a mirror. But he did not verbally acknowledge it, though he liked seeing such images and would laugh when shown one. I should think that the second milestone is also available to apes, who don't have language as we do (even the ones trained in sign language never ask questions, or tell us what they think, for example) but are capable of manipulating complex symbols to make demands.