What is the ruling on the prayer of one who doubts the rak'ah (unit of prayer) they are in while moving from one pillar to another, or while reciting Al-Fatiha, or while glorifying Allah in prostration, and then remembers during the act? And is their prayer invalidated because they acted while in doubt?

If a worshipper doubts which [cycle of prayer] (rak'ah) he is in while descending for bowing (ruku'), reciting Al-Fatihah, or prostrating, but then remembers with certainty that he is in the correct rak'ah, then his prayer is valid and he is not required to perform the prostration of forgetfulness (sujood as-sahw), as the reason for it has ceased to exist. Doubting during the performance of an act in prayer does not invalidate it, unless the doubt is regarding the intention (niyyah) or the opening takbeer (takbeerat al-ihram), because in these cases, the act would be devoid of intention.