First answer: PERFECT
Trace PERFECT across the first row: 1 at row 1, column 1; 2 at row 1, column 2; 3 at row 1, column 3; 4 at row 1, column 4; 5 at row 1, column 5; 6 at row 1, column 6; 7 at row 1, column 7.
The letters read P → E → R → F → E → C → T. Every move goes right, so this seven-cell route has no turns and consists of one straight segment. It spans all seven columns in a single row, visits seven edge cells, and includes both corner cells at its endpoints. After these seven cells are assigned, 27 open cells remain for the other three entries.
This is the only route here that never changes direction. Its starting cell has two open orthogonal neighbors on the raw board, while its ending cell has one. Once you commit to the opening P, the six consecutive rightward moves provide a clean length check: stopping before the final T would leave the entry short.