“以为(yǐwéi)” vs. “认为(rènwéi)” – Similar but Different

Please choose the correct answer to fill in the blank.
            James, nǐ  shì nǎ guó rén?
Peter:James,你 是 哪  国   人?
            James, where are you from?
             Wǒ shì Àodàlìyà rén.
James:我   是  澳大利亚 人。
             I’m Australian.
            Zhēn de ma? Wǒ ____ nǐ shì Měiguó rén.…