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In the SSL connection process, after the client successfully verifies the server's certificate, it sends a Key Exchange message. This message is crucial because it completes the negotiation of cryptographic parameters that were established during the earlier stages of the secure connection process.

The Key Exchange message allows the client and server to safely exchange the keys needed for the session encryption. This occurs after the client has confirmed the authenticity of the server by validating its certificate, ensuring that it is communicating with the intended server and not an impostor.

The other options represent different stages of the SSL handshake process. The Finished message, for instance, is sent at the end of the handshake once all necessary parameters and keys are established. The Hello message is part of the initial communication, where both parties express their protocol versions and capabilities. The Certificate message is where the server sends its certificate to the client for validation, before the client sends its own Key Exchange message.

Understanding this sequence of messages is critical for grasping the SSL handshake's structure, particularly how security is established before any sensitive information is transmitted.