A car's odometer reads $abc$ miles at the start of a journey and $cba$ miles at the end, where $abc$ and $cba$ are 3-digit numbers with $a\ge 1$. The car traveled for a whole number of hours at an average speed of 77 miles per hour. If the sum of the digits $a+b+c$ is at most 9, what is $a^2+b^2+c^2$?