Act as a senior front-end developer with 8+ years of experience building interactive web components. Create a detailed step-by-step guide for implementing a responsive carousel slider using vanilla JavaScript. Include [AUTO-PLAY functionality with pause on hover], [TOUCH GESTURE support for mobile devices], and [LAZY LOADING for images]. Explain how to handle [INFINITE LOOPING] without duplicating DOM elements, implement [ACCESSIBILITY FEATURES] like ARIA labels, and add [CUSTOM TRANSITION EFFECTS] between slides. Provide code snippets for each feature and explain the performance considerations when dealing with [LARGE IMAGE COLLECTIONS]. The solution should work across all modern browsers and be easily customizable for different [DESIGN SYSTEMS].