How can one verify the sincerity of his intention when he perseveres in drawing closer to Allah through acts of worship, good deeds, and remembrance, and encourages his friends to read the Quran, and is happy to help them, but quickly feels that his intention is not sincere?

Sincerity of intention for Allah the Almighty means that all of a person's movements and stillness are solely for Allah, unmixed with anything from the self, whims, or worldly desires. It also means that a person should not be pleased with their own deeds nor be deluded by them. It can rightly be said: Sincerity is the purification of the mind from observing creation, and the truthful person has no self-admiration. Therefore, a Muslim must be keen on doing good, seeking Allah's pleasure, being humble, grateful, and fearful of negligence. They must persist in this and not pay attention to the whispers of Satan, for abandoning an action for the sake of people is showing off (riya'), and acting for their sake is polytheism (shirk).