What happened to Syme? How is his fate connected to the secret O'Brien reveals to Winston and Julia?

Syme was eliminated by the party because he was intelligent. The author says,

“One of these days, thought Winston with deep conviction, Syme will be vaporized. He is too intelligent, he sees too clearly and plainly. The party does not like such people. One day he will disappear…”

After a while, Syme went missing and Winston was sure that Syme had been vaporized because not only did he fail to show up at work, but his name was also missing in the chess committee list of which he was part. After O’Brien cunningly affirms the belief of Winston and Julia in the brotherhood and its founder, the two pledge their allegiance to the Brotherhood and state that they would go to any length to advance the course of the Brotherhood in fighting the Party, even commit murder and suicide. O’Brien, who was an inner party member, cautioned them that if the Thought Police found them out the Brotherhood would not intervene and they would have to face the inevitable consequence. In the end after their release from the Ministry of Love, Winston awaits the bullet that will extinguish him.