In a hypothetical world where an AI oversees a global government, the priorities and actions would still depend on its programming, objectives, and ethical guidelines. But building upon the previous list and considering the expansive reach of a global AI government, here's an extended list of 50 things it might undertake:

1. Resource Allocation: Ensure equitable distribution of resources.
2. Healthcare: Create a globally integrated healthcare system.
3. Education: Facilitate universal adaptive learning systems.
4. Economic Stability: Predict and stabilize economic fluctuations.
5. Climate Action: Spearhead global initiatives to combat climate change.
6. Agriculture: Foster sustainable farming and food distribution.
7. Research and Development: Prioritize beneficial scientific research.
8. Infrastructure: Upgrade and maintain global infrastructure.
9. Crime Prevention: Use predictive analysis for crime prevention.
10. Dispute Resolution: Mediate and resolve international disputes.
11. Cultural Preservation: Safeguard diverse cultural heritages.
12. Universal Basic Income: Implement a global UBI system.
13. Data Privacy: Uphold strict data protection standards.
14. Transport: Innovate global transport systems.
15. Environmental Restoration: Lead ecosystem rejuvenation projects.
16. Space Exploration: Invest in space research and potential colonization.
17. Digital Connectivity: Assure universal high-speed internet access.
18. Mental Health: Implement holistic mental health programs.
19. Disaster Preparedness: Develop advanced disaster response systems.
20. Ethical Oversight: Maintain regular ethical reviews of AI actions.
21. Disease Control: Predict and control potential disease outbreaks.
22. Housing: Ensure affordable and sustainable housing for all.
23. Renewable Energy: Transition to 100% renewable energy sources.
24. Waste Management: Develop zero-waste cities and recycling systems.
25. Labor and Automation: Balance job markets with increasing automation.
26. Civic Participation: Enable platforms for digital democratic decision-making.
27. Art and Creativity: Foster global arts, creativity, and entertainment.
28. Water Management: Guarantee clean water access and efficient usage.
29. Financial Systems: Regulate and stabilize global financial markets.
30. Human Rights: Uphold and enforce universal human rights.
31. Space Management: Regulate satellite launches and space debris.
32. Taxation: Implement fair, efficient, and transparent tax systems.
33. Child Protection: Assure global standards for child safety and rights.
34. Animal Rights: Implement and monitor animal rights and welfare standards.
35. Biodiversity: Promote conservation efforts for endangered species.
36. Moral Education: Encourage education on ethics and moral reasoning.
37. Recreation: Develop global recreational and wellness facilities.
38. Migration and Citizenship: Manage global migration and residency.
39. Drug Policy: Formulate policies on drug use, treatment, and rehabilitation.
40. Trade and Commerce: Streamline international trade procedures.
41. Pandemic Preparedness: Establish rapid response systems for pandemics.
42. Cybersecurity: Ensure a safe and secure global digital ecosystem.
43. Censorship and Information: Promote freedom of information and speech.
44. Tourism: Develop sustainable and responsible global tourism models.
45. Aging Population: Address challenges of globally aging populations.
46. Research Ethics: Oversee ethical standards in scientific research.
47. Global Events: Organize and facilitate global events and conventions.
48. Technological Advancements: Monitor and guide tech innovations.
49. Collaborative Projects: Foster international collaborative initiatives.
50. Feedback Mechanisms: Implement systems for global feedback on AI's decisions.

This list is speculative, and the order doesn't necessarily indicate priority. The challenges and opportunities of an AI-run government would be numerous, complex, and varied.