Could you write me a todo list management web application where:

• I can have my todo list displayed.
• I can manipulate my list (add/remove/modify entries).
• Assign priorities and due dates to the entries.
• I can sort my entry lists using due date and priority.
• I can mark an entry as completed.
• Minimal UI/UX design is needed.
• I need every client operation done using JavaScript, reloading the page is not an option.
• Write a RESTful API which will allow a third-party application to trigger actions on your app (same actions available on the webpage).