inquam

Inquam is defective: it exists in a short list of forms and nothing else. Present inquam, inquis, inquit, inquimus, inquitis, inquiunt, a future inquies and inquiet, an imperative inque, and a perfect inquit identical to the present. There is no infinitive, so you cannot say inquire in this sense, and no participle.

Its other rule is positional, and it is absolute: inquam never opens a sentence. It goes inside the quotation, after the first word or two, exactly where English puts "he said". Veni, inquit, et vide. That parenthetical habit is the whole reason the verb survives alongside dico, which does all the ordinary work of saying, and aio, which is also defective but reports rather than quotes. The clash of present and perfect inquit is resolved by context alone.