Here's how I've coded this app. Any tips on how to improve it?

# Create list
shopping_list = []

# Show help
def show_help():
    print("Here's what you can do:")
    print("- Type SHOW to see your current list.")
    print("- Type ADD to see your current list.")
    print("- Type REMOVE to remove an item from your list.")
    print("- Type STOP to quit the app.")
    print("- Type HELP to see these instructions again.")
    print("=" * 30)

# Add new item
def add_new():
    print("Tip: You can add more than one item by separating them with commas.")
    item = input("Describe the new item: ")
    if len(item.split(",")) == 1:
        shopping_list.append(item)
        print("New item added!")
    else:
        shopping_list.extend(item.split(','))
        print("New items added!")

# Remove item
def remove_item():
    if len(shopping_list) == 0:
        print("Your list is empty!")
        return False
    item = input("Tell me which item you'd like to remove: ")
    try:
        shopping_list.remove(item)
    except ValueError:
        print("This item is not on your list!")
    else:
        print("Item removed!")

# Show list
def show_list():
    if len(shopping_list) != 0:
        for index, item in enumerate(shopping_list):
            print("{}. {}".format((index + 1), item))
    else:
        print("Your list is empty!")

show_help()

# Loop
while True:
    action = input("> ").upper()
    if action == "SHOW":
        show_list()
        print("=" * 30)
        continue
    elif action == "ADD":
        add_new()
        print("=" * 30)
        continue
    elif action == "REMOVE":
        remove_item()
        print("=" * 30)
        continue
    elif action == "HELP":
        show_help()
        continue
    elif action == "DONE":
        print("Bye!")
        break
    else:
        print("That's not a valid action!")
        print("=" * 30)
        continue