Rawski writes that Altan Khan's conversion to the Gelug "can be interpreted as an attempt to expand his authority in his conflict with his nominal superior, Tümen Khan." To further cement the Mongol-Tibetan alliance, the great-grandson of Altan Khan—the 4th Dalai Lama (1589–1616)—was made the fourth Dalai Lama. In 1642, the 5th Dalai Lama (1617–1682) became the first to wield effective political control over Tibet.

Who was Altan Khan's nominal superior?