What changes at every step
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Step 1PERM -> PERP
Tile 4 changes M to P; the move is closer by letter shape. PERP has 5 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from PERM include PERT, PERK, TERM, GERM.
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Step 2PERP -> PEEP
Tile 3 changes R to E; the move is sideways by letter shape. PEEP has 13 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from PERP include PERT, PERK, PARP.
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Step 3PEEP -> PREP
Tile 2 changes E to R; the move is sideways by letter shape. PREP has 4 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from PEEP include KEEP, DEEP, PEER, PEEL.
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Step 4PREP -> PROP
Tile 3 changes E to O; the move is closer by letter shape. PROP has 11 legal neighbors, 1 shortest continuation, and 1 move remaining. Other legal exits from PREP include PREY, PREZ.
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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, CROP, PROS.