The newbie assignment is a solid start.
There is something you can do in parallel as well, and that is to go out more with your friends, and have them invite some of their friends that you don't know (mainly women of course). This will give you more experience talking to women in general, and maybe you'll even hit it off with some of them.
It's gonna be difficult at first, but once you do it, you will start to see the feeling you used to consider approach anxiety as excitement to meet a new beautiful girl. And no matter what the result of the interaction is, the important thing is that you did your duty as a man, because you simply have very little control over how she responds after your approach.
If you don't want to do the newbie assignment right away, there is another assignment you can do to get started. My friend Kaylan gave me this one and it's what got me back into approaching. Here it is:
Over the next week, you have to approach 10 new girls, give them a genuine compliment, wish them a good day and leave. If you want to continue the conversation you absolutely can. So you do the math, how many girls you have to approach each day.
When I was starting with it I went to a park and starting walking around, there were beautiful women everywhere, but I couldn't approach. Eventually I saw a very beautiful french girl sitting on a bench working on her laptop. I walked past her, sat on another bench, and said to myself "Fuck it, I'm gonna do it". I walked up to her, gave her the compliment, she smiled and said thank you, then I left. The feeling was amazing, and it was at that moment that I realized that I've just done a direct cold approach during the day! I felt unstoppable! Later on I approached another girl, who had headphones on. This time we chatted for a bit and then we parted ways.
So you can do it, you just have to set a goal and work for it, and trust me you'll feel amazing afterwards.