What changes at every step
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Step 1PAID -> PAIL
Tile 4 changes D to L; the move is sideways by letter shape. PAIL has 14 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from PAID include SAID, PAIN, PAIR, LAID.
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Step 2PAIL -> PALL
Tile 3 changes I to L; the move is sideways by letter shape. PALL has 16 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from PAIL include FAIL, TAIL, MAIL, PAIN.
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Step 3PALL -> POLL
Tile 2 changes A to O; the move is closer by letter shape. POLL has 12 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from PALL include PULL, PILL, CALL, FALL.
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Step 4POLL -> POOL
Tile 3 changes L to O; the move is closer by letter shape. POOL has 8 legal neighbors, 1 shortest continuation, and 1 move remaining. Other legal exits from POLL include ROLL, TOLL, PULL, PILL.
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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, TOOL, COOL.