I just re-started Atkins today, after doing my own thing for a while. I need to get oriented again on the very clean basics. Time to pull out my book!
Okay, my 2002 book says 2-3 cups loosely packed salad vegetables (from the list) plus 1 cup of cooked vegetables (from a second list, that has a few of the same veggies from the first list.) A typical salad for me consists in a cup of lettuce, a few chunks of tomato, some green bell peppers, olives, and olive oil for dressing. Two of those a day don't get anywhere close to 12 NC. And a cup of broccoli cooked has slightly less than 4 NC.
I notice a suggestion to eat half an avocado, and 10 olives. That would bring the count up a bit.