Hello @ITGUY2013
The WAN IP address will be assigned by your internet service provider (assuming you don't have an "outer" NAT router – i.e., "double NAT"). But, from the rest of your question, I'll assume you mean the LAN IP address range that the Nest WiFi Pro primary/router unit uses to assign addresses to "inner" network devices on the network it creates.
The answer is that you can't choose something random. The IETF (Internet Engineering Task Force, the standards body that creates and maintains all of the standards that make the internet work) has documented the "Private" IPv4 addresses that can safely be used in networks like these. The specification for that address space is in RFC 1918, which includes an 8-bit netmask space from 10.0.0.0 to 10.255.255.255, a 12-bit netmask space from 172.16.0.0 to 172.31.255.255, and a 16-bit netmask space from 192.168.0.0 to 192.168.255.255. It is this latter space that most home routers use, but with a wider netmask, typically 24 bits, enabling about 250 addresses to be assigned to local devices. That's why you see a lot of home routers use local networks that look like 192.168.0.x or 192.168.1.x. It's important to use addresses in one of these ranges since you can't communicate with a machine on the public internet using the same IP address as your local network.
I can't say why Google chose 192.168.86.x for their network address range, but I can speculate that in a double NAT situation, using something other than 192.168.0.x makes it less likely they'd have to automatically pick something different on the fly.
Routing is somewhat complex, especially when NAT firewalls are in the picture. But, I hope this helps a bit!
