How do i get a new ip address with verizon?

Im looking to get a new external ip address. I have verizon fios intenet. The router is the standard one that verizon gives out (Actiontec MI-424-WRv2). So far i have read that turning the router off could give you a new ip. I turned it off for about 45 minutes and when i turned it back on i had the same ip. I also read that you can refresh your DHCP settings and that might give you a new ip, but i cant figure out how to do this with this router. Any ideas?
Thanks for the tips Bob, but it didnt work. I need to change the external ip. The one thats something like 75.103.222.XXX. I think what you told me, resets my internal ip, the one thats like 192.168.0.1 or whatever.

The only legal way to get a new IP is to make a written request to your ISP (Verizon) If your request was reasonable they should do it for you either free or for some cost. Contact your customer care for more details. If your IP has been changed, Your ISP would inform you by mail or any other medium. You can also visit www.IP-Details.com to ensure that your IP address is changed.