What changes at every step
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Step 1SLUM -> SLUR
Tile 4 changes M to R; the move is sideways by letter shape. SLUR has 5 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from SLUM include SLIM, SLAM, SLUG, GLUM.
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Step 2SLUR -> SOUR
Tile 2 changes L to O; the move is closer by letter shape. SOUR has 12 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from SLUR include SPUR, SLUG, BLUR.
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Step 3SOUR -> POUR
Tile 1 changes S to P; the move is closer by letter shape. POUR has 9 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from SOUR include YOUR, FOUR, TOUR, HOUR.
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Step 4POUR -> POOR
Tile 3 changes U to O; the move is closer by letter shape. POOR has 7 legal neighbors, 1 shortest continuation, and 1 move remaining. Other legal exits from POUR include YOUR, FOUR, TOUR, HOUR.
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Step 5POOR -> POOP
Tile 4 changes R to P; the move is closer by letter shape. POOP has 11 legal neighbors, target reached, and 0 moves remaining. Other legal exits from POOR include POOL, POOF, DOOR, MOOR.