What changes at every step
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Step 1HULA -> HULL
Tile 4 changes A to L; the move is sideways by letter shape. HULL has 15 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from HULA include PULA, HULK.
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Step 2HULL -> PULL
Tile 1 changes H to P; the move is closer by letter shape. PULL has 15 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from HULL include FULL, HILL, HALL, NULL.
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Step 3PULL -> POLL
Tile 2 changes U 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 PULL include PILL, PULP, PALL, FULL.
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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, PILL, DOLL.
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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.