Soon after the victory in Ü-Tsang, Güshi Khan organized a welcoming ceremony for Lozang Gyatso once he arrived a day's ride from Shigatse, presenting his conquest of Tibet as a gift to the Dalai Lama. In a second ceremony held within the main hall of the Shigatse fortress, Güshi Khan enthroned the Dalai Lama as the ruler of Tibet, but conferred the actual governing authority to the regent Sonam Chöpel. Although Güshi Khan had granted the Dalai Lama "supreme authority" as Goldstein writes, the title of 'King of Tibet' was conferred upon Güshi Khan, spending his summers in pastures north of Lhasa and occupying Lhasa each winter. Van Praag writes that at this point Güshi Khan maintained control over the armed forces, but accepted his inferior status towards the Dalai Lama. Rawski writes that the Dalai Lama shared power with his regent and Güshi Khan during his early secular and religious reign. However, Rawski states that he eventually "expanded his own authority by presenting himself as Avalokiteśvara through the performance of rituals," by building the Potala Palace and other structures on traditional religious sites, and by emphasizing lineage reincarnation through written biographies. Goldstein states that the government of Güshi Khan and the Dalai Lama persecuted the Karma Kagyu sect, confiscated their wealth and property, and even converted their monasteries into Gelug monasteries. Rawski writes that this Mongol patronage allowed the Gelugpas to dominate the rival religious sects in Tibet.
How long did it take for Gyatso to travel to his welcoming ceremony organized by Khan?
a day