Final answer:
President Reagan would be convinced of the Soviet Union's move towards a more progressive future through concrete actions taken by Soviet leader Mikhail Gorbachev, such as engaging in arms reduction talks, implementing perestroika and glasnost reforms, and signing the INF Treaty to reduce nuclear weapons.
Step-by-step explanation:
What would convince President Reagan that the Soviet Union is making positive changes towards a more progressive future? President Ronald Reagan's approach to foreign policy, particularly concerning the Soviet Union, was initially characterized by a desire to achieve "peace through strength."
However, his views began to evolve with the ascendancy of Mikhail Gorbachev as the General Secretary of the Soviet Communist Party. Gorbachev recognized the need for reform in the Soviet Union due to economic strains, particularly those stemming from military expenditures and the war in Afghanistan.
Significant actions taken by Gorbachev that would indicate positive change to Reagan included withdrawing troops from Afghanistan, initiating political reforms and civil liberties through perestroika and glasnost, and entering into arms reduction talks with the United States.
In 1985, the willingness of Gorbachev to discuss the reduction of armaments and shrink military budgets during the Geneva summit presented a hopeful sign to Reagan. The subsequent Reykjavík meeting in 1986, where both leaders expressed the desire to eliminate nuclear weapons, demonstrated further commitment to a more progressive future.
In 1987, the signing of the Intermediate-Range Nuclear Forces (INF) Treaty marked a concrete step towards this new direction, signifying a major policy shift that was aligned with Reagan's visions of diplomatic progress and mutual reduction of nuclear capabilities.