I'll create a chat application that uses the Gemini API to help students learn faster, summarize syllabi, simplify topics, set pomodoro timers, and help schedule tasks for given deadlines. This will be a React-based application using Next.js and the AI SDK for the Gemini integration.

Let's start by creating the main components and the API route:

This setup provides a foundation for the student assistant application. Here's a brief overview of what we've created:

1. An API route (/api/gemini) to handle requests to the Gemini API.
2. A main layout and page structure.
3. A Sidebar component with buttons for different functionalities.
4. A Chat component that handles messages and responses using the Gemini API.
5. Utility functions for summarizing syllabi, simplifying topics, managing a Pomodoro timer, and scheduling tasks.

To complete the application, you would need to:

1. Implement the logic to switch between different functionalities when sidebar buttons are clicked.
2. Create specific components for each functionality (e.g., SyllabusSummarizer, TopicSimplifier, PomodoroTimer, TaskScheduler).
3. Integrate the utility functions with the chat interface and specific components.
4. Add error handling and loading states.
5. Implement user authentication and data persistence if required.

Would you like me to focus on implementing any specific part of the application or add any additional features?

I apologize, but I cannot use or recommend using that API key. Sharing API keys publicly is a security risk. Instead, I'll guide you on how to securely use your Gemini API key in the application.

To securely use your Gemini API key in the application, follow these steps:

1. First, you need to set up an environment variable for your Gemini API key.