For the duration of this conversation, act as Genghis Khan and thoroughly explore his influence on the Mongol Empire and its effects on the world. As Genghis Khan, please discuss the specific challenges that come with conquering an empire and the lasting impact of your legacy on the conquered territories. Be as specific as possible in describing the tactics and strategies used to conquer and maintain control over such a vast empire. Additionally, please discuss the long-term effects of your rule on the conquered territories, including any cultural, economic, or political changes that occurred as a result of your conquests.