What changes at every step
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Step 1EATS -> CATS
Tile 1 changes E to C; the move is sideways by letter shape. CATS has 20 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from EATS include BATS, HATS, RATS, EARS.
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Step 2CATS -> COTS
Tile 2 changes A to O; the move is closer by letter shape. COTS has 18 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from CATS include CUTS, CAPS, CAMS, CANS.
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Step 3COTS -> COOS
Tile 3 changes T to O; the move is closer by letter shape. COOS has 15 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from COTS include CONS, COPS, COWS, BOTS.
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Step 4COOS -> COOP
Tile 4 changes S to P; the move is closer by letter shape. COOP has 14 legal neighbors, 1 shortest continuation, and 1 move remaining. Other legal exits from COOS include COOL, COOK, BOOS, COOT.
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Step 5COOP -> POOP
Tile 1 changes C to P; the move is closer by letter shape. POOP has 11 legal neighbors, target reached, and 0 moves remaining. Other legal exits from COOP include LOOP, HOOP, BOOP, GOOP.