mình is correct, perhaps you should support that sentence. But I remember reading on Duolingo that you should only say "tôi" and any other usage and translation would not be accepted. I am a Vietnamese native speaker and I don't know why. But if you were about to say "con mèo của mình ủng hộ tôi"(makes no sense) or "con mèo của tôi ủng hộ mình"(changes the meaning and becomes my cat supports itself and still sounds weird, perhaps con mèo của tôi ủng hộ chính mình/con mèo của tôi ủng hộ bản thân nó sounds better. You need to use either "mình" or "tôi". For example: "con mèo của tôi ủng hộ tôi" or "con mèo của mình ủng hộ mình". You may say "tớ" as well. "ta" and "tao" both are used to show that you are at a higher position than the one you're talking with. Especially, "ta" is used in a joking manner and sartorially as it has a very old meaning, just like when you say "thee, thou, thy" instead of "you". Nowadays people use it as a funny way to point towards themselves as"tôi/mình/tớ" and it is also widely used as a short form of "chúng ta" to make it sound like an idiom or a term for ex: lịch ta(our calendar=lunar calendar) nước ta(our country) hàng ta tốt hơn hàng ngoại(our goods are better than foreign goods). So does the word "mình" you may say "mình" as a short form of "chúng mình". "Mình" and "ta" are a little bit different but it would be hard for non-native speakers to "feel" the difference, when you become fluent you would know. By the way, be aware that "mình" is used to show that you are at the same position as the one you're talking with. Happy studying!

That's what I want to know...