What changes at every step
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Step 1TALE -> TALL
Tile 4 changes E to L; the move is sideways by letter shape. TALL has 15 legal neighbors, 2 shortest continuations, and 4 moves remaining. Other legal exits from TALE include PALE, TAME, TOLE, TAKE.
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Step 2TALL -> TOLL
Tile 2 changes A to O; the move is closer by letter shape. TOLL has 12 legal neighbors, 2 shortest continuations, and 3 moves remaining. Other legal exits from TALL include PALL, CALL, TELL, FALL.
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Step 3TOLL -> TOOL
Tile 3 changes L to O; the move is closer by letter shape. TOOL has 9 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from TOLL include POLL, ROLL, DOLL, TOIL.
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Step 4TOOL -> POOL
Tile 1 changes T to P; the move is closer by letter shape. POOL has 8 legal neighbors, 1 shortest continuation, and 1 move remaining. Other legal exits from TOOL include COOL, WOOL, FOOL, TOOK.
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Step 5POOL -> POOP
Tile 4 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 POOL include POOR, POOF, COOL, POLL.