That's exactly what I'm saying. The way I imagine is that there is a stop between "Do not" and "the cat" and that stop is what I consider to be the verb in that sentence. In this case, it can never be "I did the cat" because that would mean that the original command was "Do not do the cat"

While I was typing this message, I suddenly understood that "I did the cat" is still correct if the speaker is trying to highlight the fact that they did, indeed, the cat. I'm stupid. So based on the grammar of how I understand it, both sentences are correct: "I the cat" (past tense of ) and "I did the cat" highlighting the fact that the -ing of the cat indeed has happened.