Final answer:
The correct verb form is 'vayas'.
Step-by-step explanation:
The correct verb form that completes the conversation is vayas. In this conversation, Carolina is suggesting that Diego goes to the library to look for the book. Since Diego is the one being suggested to go, the correct verb form is second person singular, vayas. This form matches the subject 'tú' (you) in Spanish.
Learn more about Spanish verb forms