New chat started from template Next.js + shadcn/ui

I'll add a mock authentication system to your Next.js application. This will include a simple login page, a protected dashboard, and a mock authentication context. We'll use React's Context API for state management and Next.js App Router for routing.

Let's start by creating the necessary components and context:

This setup provides a basic mock authentication system with the following features:

1. A login page at /login
2. A protected dashboard at /dashboard
3. Authentication state management using React Context
4. Mock login/logout functionality
5. Persistence of login state using localStorage

To test the authentication:

1. Navigate to the home page, which will redirect to /login
2. Use the username "user" and password "password" to log in
3. You'll be redirected to the dashboard upon successful login
4. The logout button on the dashboard will log you out and redirect you back to the login page

Remember, this is a mock authentication system and is not secure for production use. In a real application, you would want to implement proper server-side authentication and use secure methods for storing and transmitting credentials.