zakirkun/lms ? reverse-engineered prompt

Build me a clean learning management system web app where teachers can create and manage courses, add lessons and other content, and keep track of students and instructors. Students should be able to sign in, browse their courses, view course details, submit assignments, and see their progress over time. I also want basic real time notifications and a simple admin style experience for managing users and content.

Use a modern Next.js app with Supabase for login, database, and file storage, and make it feel polished and responsive like a real product. Please include a nice home page, a course listing page, and a detailed course view that looks good on desktop and mobile. If you need to check current docs or best practices for Supabase or Next.js, look them up online first.