What changes at every step
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Step 1LASH -> LAST
Tile 4 changes H to T; the move is sideways by letter shape. LAST has 13 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from LASH include CASH, BASH, LUSH, RASH.
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Step 2LAST -> LOST
Tile 2 changes A to O; the move is closer by letter shape. LOST has 13 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from LAST include LIST, CAST, LUST, LEST.
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Step 3LOST -> LOOT
Tile 3 changes S to O; the move is closer by letter shape. LOOT has 16 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from LOST include COST, HOST, LOFT, LOUT.
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Step 4LOOT -> LOOP
Tile 4 changes T to P; the move is closer by letter shape. LOOP has 9 legal neighbors, 1 shortest continuation, and 1 move remaining. Other legal exits from LOOT include LOOK, BOOT, LOOM, LOON.
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Step 5LOOP -> POOP
Tile 1 changes L to P; the move is closer by letter shape. POOP has 11 legal neighbors, target reached, and 0 moves remaining. Other legal exits from LOOP include COOP, HOOP, BOOP, GOOP.