What changes at every step
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Step 1GRAN -> GRAM
Tile 4 changes N to M; the move is sideways by letter shape. GRAM has 10 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from GRAN include GRAD, GRAY, GRAB, GRIN.
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Step 2GRAM -> PRAM
Tile 1 changes G to P; the move is closer by letter shape. PRAM has 8 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from GRAM include GRAD, GRIM, DRAM, TRAM.
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Step 3PRAM -> PROM
Tile 3 changes A to O; the move is closer by letter shape. PROM has 9 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from PRAM include PRIM, PRAY, DRAM, TRAM.
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Step 4PROM -> PROP
Tile 4 changes M to P; the move is closer by letter shape. PROP has 11 legal neighbors, 1 shortest continuation, and 1 move remaining. Other legal exits from PROM include PROS, PROF, PROD, PROG.
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Step 5PROP -> POOP
Tile 2 changes R to O; the move is closer by letter shape. POOP has 11 legal neighbors, target reached, and 0 moves remaining. Other legal exits from PROP include PLOP, DROP, CROP, PREP.