This is a fare so low that I am tempted to buy a visa for Brazil and check out the country for the first time. Yesterday American dropped LAX-GRU Sao Paulo to $557 and this morning Delta countered with $513 and now American has dropped the fare again to as low as $443 round trip.
You can fly nonstop LAX-GRU or possibly route through New York JFK for more miles.
$442.24 Los Angeles – Sao Paulo Brazil GRU
12,312 flight miles
$446.74 Los Angeles – Miami MIA – Sao Paulo Brazil GRU – LAX
12,570 flight miles