Harder Sudoku

Ok, let's see if our algorithm will work all the time. Here's a harder sudoku puzzle:

grid2 = '4.....8.5.3..........7......2.....6.....8.4......1.......6.3.7.5..2.....1.4......'
values = grid_values(grid2)

When we apply reduce_puzzle, we get the following grid:

Oh no! The algorithm didn't solve it. It seemed to reduce every box to a number of possibilites, but it won't go farther than that. We need to think of other ways to improve our solution.