Vertical Infinite Slider - Copy this Html, Tailwind Component to your project

Create a vertical menu with an infinite slider for the options using HTML, CSS, and JavaScript. The menu should be styled to have a clean, modern look with a subtle hover effect on the options. The slider should automatically cycle through the menu options without any user input, but the user should also be able to manually scroll through the options by hovering over the menu. The menu options should loop infinitely when the slider reaches the end or start.