What changes at every step
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Step 1NEXT -> NEAT
Tile 3 changes X to A; the move is sideways by letter shape. NEAT has 12 legal neighbors, 2 shortest continuations, and 5 moves remaining. Other legal exits from NEXT include NEST, TEXT, NEWT.
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Step 2NEAT -> BEAT
Tile 1 changes N to B; the move is sideways by letter shape. BEAT has 20 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from NEAT include PEAT, NEAR, HEAT, SEAT.
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Step 3BEAT -> BOAT
Tile 2 changes E to O; the move is closer by letter shape. BOAT has 11 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from BEAT include BEAR, BELT, PEAT, BRAT.
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Step 4BOAT -> BOOT
Tile 3 changes A to O; the move is closer by letter shape. BOOT has 20 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from BOAT include COAT, BOLT, BOUT, BOAR.
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Step 5BOOT -> BOOP
Tile 4 changes T to P; the move is closer by letter shape. BOOP has 12 legal neighbors, 1 shortest continuation, and 1 move remaining. Other legal exits from BOOT include BOOK, BOOB, BOOM, BOON.
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Step 6BOOP -> POOP
Tile 1 changes B to P; the move is closer by letter shape. POOP has 11 legal neighbors, target reached, and 0 moves remaining. Other legal exits from BOOP include LOOP, COOP, HOOP, GOOP.