From Wiktionary, the free dictionary
Literally "asked himself".
שָׁאַל אֶת עַצְמוֹ • (sha'ál et atsmó) (pa'al construction)
- (He/it) wondered (pondered with curiosity).
The verb is conjugated like שָׁאַל, and עַצְמוֹ inflects according to the agent (subject).