Try it this way

Your initialize block should be set to create empty list.
What you have now in your initialize block should go into a set websites block in your next button click event handler . There are better ways; this might work and it is minimal changing of your blocks. Try it if it does not work, show what you tried .
Also you are switching screens. Bad idea but do what you want to do , better to use virtual screens ... see
If you take the time to read the resources mentioned below, you would have known how to do this We want you to have fun with App Inventor so here are some resources to help you learn to use the AI2 tools A very good way to learn App Inventor is to read the free Inventor's Manual here in the AI2 free online eBook
http://www.appinventor.org/book2 ... the links are at the bottom of the Web page. The book 'teaches' users how to program with AI2 blocks.
Just try some blocks and have fun.
Regards,
Steve