Country Connect by Last Two Neighbors

Start with Chile and Argentina.
Find the country (not guessed) (number it 3) that borders both those countries.
Then, find a country that borders Argentina and country #3.
Then find a country #5 that borders country #3 and country #4, and continue until you guess all countries.

Technicalities

1. Assume all unguessed countries are candidates.
2. Start with the highest # country.
3. If any candidate(s) border that country, narrow the candidates down to those neighboring candidates.
4. Else, keep the candidates as is.
5. Repeat for the next highest # country.
6. Continue until one candidate is left, and guess it.
7. If you get through all #-countries with multiple candidates, choose the (geographically) biggest one.