What changes at every step
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Step 1CANT -> CAST
Tile 3 changes N to S; the move is sideways by letter shape. CAST has 14 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from CANT include CANS, CART, CANE, WANT.
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Step 2CAST -> COST
Tile 2 changes A to O; the move is closer by letter shape. COST has 11 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from CAST include LAST, CYST, CASE, CART.
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Step 3COST -> COOT
Tile 3 changes S to O; the move is closer by letter shape. COOT has 17 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from COST include LOST, HOST, COAT, COLT.
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Step 4COOT -> COOP
Tile 4 changes T 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 COOT include COOL, COOK, BOOT, LOOT.
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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.