What changes at every step
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Step 1TRAY -> TRAP
Tile 4 changes Y to P; the move is closer by letter shape. TRAP has 6 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from TRAY include PRAY, TRAM, TRAD, CRAY.
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Step 2TRAP -> CRAP
Tile 1 changes T to C; the move is sideways by letter shape. CRAP has 10 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from TRAP include TRIP, WRAP, TRAM, TRAD.
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Step 3CRAP -> CROP
Tile 3 changes A to O; the move is closer by letter shape. CROP has 8 legal neighbors, 2 shortest continuations, and 2 moves remaining. Other legal exits from CRAP include CHAP, CLAP, WRAP, CRAB.
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Step 4CROP -> PROP
Tile 1 changes C to P; the move is closer by letter shape. PROP has 11 legal neighbors, 1 shortest continuation, and 1 move remaining. Other legal exits from CROP include COOP, DROP, CHOP, CLOP.
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Step 5PROP -> POOP
Tile 2 changes R to O; the move is closer by letter shape. POOP has 11 legal neighbors, target reached, and 0 moves remaining. Other legal exits from PROP include PLOP, DROP, PREP, PROS.