Step 1: Parasomnias divide neatly by sleep phase. Arousal parasomnias such as somnambulism cluster in the deepest part of NREM, which is the slow-wave stages 3 and 4.
Step 2: Alongside walking in sleep, the same deep stage produces night terrors with screaming and autonomic arousal, bed wetting, teeth grinding and talking in sleep. A shared clue is poor recall of the episode afterwards.
Step 3: REM is the opposite end of the spectrum and is where dreaming, nightmares and narcolepsy-related events sit, so option REM is excluded. The lighter stages 1-2 and the 2-3 transition lack the deep slow-wave activity needed for somnambulism.
Step 4: Mapping the parasomnia to its phase confirms the deepest NREM stages.
\[\boxed{\text{Stage 3-4 NREM}}\]