Develop a Next.js application featuring an AI chatbot. The chatbot should utilize the Google Gemini API, specifically leveraging the Gemini Flash 2.5 model for its responses. Implement user authentication to secure the chatbot, allowing users to log in and access the AI functionality. The authentication process should support Google sign-in. The application should have a user-friendly interface, enabling seamless interaction with the chatbot. The design should be responsive, ensuring optimal viewing across various devices. The application should also include error handling to manage potential issues with the API or authentication.