"Fun with Functions" (Python Basic Stage 5) - problem implementing within menu

shopping_list = []

def show_help():
    print("What should we pick up at the store?")
    print("Enter DONE to stop. Enter HELP for help."""
          """Enter SHOW to see your current list. Enter ADD to see contents""")

def add_to_list(item):
    shopping_list.append(item)
    print("Added! List has {} items".format(len(shopping_list)))

def show_list():
    print("Here's your list:")
    for item in shopping_list:
        print(item)

def add_list(list_num):
    total = 0
    for num in list_num:
        total += num
    return total

def summarize(list_num):
  sum = add_list(list_num)
  print("The sum of {} is {}.".format(list_num, sum))

show_help()

while True:
    new_item = input("> ")
    if new_item == "DONE":
        break
    elif new_item == "done":
        break
    elif new_item == "HELP":
        show_help()
        continue
    elif new_item == "SHOW":
        show_list()
        continue
    elif new_item == "ADD":
        summarize(shopping_list) #unsupported operand type(s) for +=: 'int' and 'str'
        continue

    add_to_list(new_item)
    continue

show_list()