I saw Kyoko went out of city hall.
I saw Kyoko go out of city hall.
I thought 'went' is the correct answer Why it has to be 'go'? Can anyone explain this to me
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Although the action happened in the past, you don't use went. See is a verb of perception and in this case it should be object + bare infinitive: I saw Kyoko go out of city hall. This means that Kyoko left city hall and you saw it.
However, go out of city hall sounds strange to me. Perhaps with more context it might sound better, but I agree with the comments. I think you should use a different verb like leave, exit, come out, walk out, etc.