Is it permissible for someone who doubts having performed the second prostration (sujud) to perform it immediately without trying to recall whether he had performed it or not, and what should he have done in this case?

The jurists differed regarding someone who doubts whether they omitted a pillar: must they investigate, or should they perform the doubted pillar based on certainty without investigation? There are two opinions among the scholars on this matter. The preponderant view is that whoever doubts having omitted a pillar is as if they have omitted it, and they must perform the doubted pillar based on certainty, due to the hadith of Abu Sa'id al-Khudri, raised to the Prophet (PBUH): "If one of you doubts in his prayer and does not know whether he prayed three or four (rak'ahs), he should cast away doubt and build upon what he is certain of." And the hadith of Ibn Mas'ud, raised to the Prophet (PBUH): "If one of you doubts in his prayer, let him strive to ascertain what is correct and complete it upon that, then greet, then prostrate twice (for the prostrations of forgetfulness)." Therefore, there is no blame on someone who performs the prostration they doubted without investigating.