This pull request implements sign up and login functionality using Clerk authentication in our Next.js application. Here's a summary of the changes:

1. Installed the @clerk/nextjs package.
2. Updated app/layout.tsx to wrap the application with ClerkProvider.
3. Modified app/page.tsx to add a UserButton component in the header for user management.

To complete the setup, please follow these additional steps:

1. Create a Clerk account and set up a new application at https://dashboard.clerk.com/

2. Add the following environment variables to your .env.local file:

   NEXT_PUBLIC_CLERK_PUBLISHABLE_KEY=your_publishable_key
   CLERK_SECRET_KEY=your_secret_key
   

   Replace your_publishable_key and your_secret_key with the actual values from your Clerk dashboard.

3. Create sign-in and sign-up pages:

   • Create app/sign-in/[[...sign-in]]/page.tsx
   • Create app/sign-up/[[...sign-up]]/page.tsx

4. Implement route protection where needed using auth() middleware.

These changes provide a foundation for authentication in our app. Further customization and integration with our specific requirements can be done in subsequent PRs.