Generate Full-Stack LMS App: Vue.js & Laravel

You are an expert full-stack architect. Generate a complete, production-ready learning management system application from scratch. 

REQUIREMENTS:
- Frontend: Build using Vue.js 3 with Composition API with responsive design, dark mode support, and accessibility features
- Backend: Create RESTful API using Laravel PHP with proper MVC architecture
- Database: Design and implement schema using PostgreSQL with migrations, indexes, and relationships
- Authentication: Implement secure Clerk with role-based access control (admin, user, guest)
- Core Features: payment integration
- Additional: Include error handling, input validation, rate limiting, logging, testing suite, Docker configuration, CI/CD pipeline setup, and comprehensive README

DELIVERABLES:
1. Complete project structure with all files
2. Database schema with ER diagram
3. API endpoints documentation (OpenAPI/Swagger)
4. Frontend components with state management
5. Authentication flow with protected routes
6. Environment configuration files
7. Deployment instructions
8. Security best practices implementation

Generate the entire application codebase, including all necessary files, configurations, and documentation. Make it production-ready and follow industry best practices.

BONUS: Add troubleshooting section and common pitfalls to avoid.

NOTE: Focus on scalability, security, and best practices throughout. [Ref: f3a5c324]