Final answer:
Kublai Khan's reign was marked by the consolidation of Mongol rule in China and the establishment of the Yuan dynasty, not by successful invasions in Southeast Asia or the division of the empire into four kingdoms.
Step-by-step explanation:
The Reign of Kublai Khan
The reign of Kublai Khan saw significant developments and changes within the Mongolian Empire. However, it was not characterized by successful invasions of Vietnam and Burma, nor by the retreat of Mongol forces from southern China, nor the division of Chinggis Khan's empire into four kingdoms. Instead, the reign of Kublai Khan led to the consolidation of Mongol rule in China, under the establishment of the Yuan dynasty. Kublai Khan's authority helped to unite China after defeating the last pockets of Song resistance and claiming the "Mandate of Heaven" as the leader of a new dynasty. Despite the earlier splitting of the Mongol Empire into separate khanates – a process known as the Toluid wars – Kublai Khan's domination over China remained solid until the end of his reign.
Sporadic efforts to expand the empire were met with difficulty. Mongol armies struggled in Southeast Asia due to the climate and terrain, hindering their traditional cavalry warfare. The Yuan dynasty under Kublai did attempt military campaigns in Southeast Asia, but these endeavors were not marked by success. The death of Kublai Khan led to a period of decline, with subsequent Yuan emperors facing internal division and declining authority, setting the stage for the eventual rise of the Ming dynasty.