Final answer:
Mikhail Gorbachev was the Soviet leader who implemented policies of glasnost and perestroika, leading to the withdrawal of Soviet forces from Eastern Europe and discussions on free-market systems, which contributed to the end of the Cold War.
Step-by-step explanation:
The amazing new Soviet leader who began to shrink the size of the Russian military, withdraw Soviet forces from Eastern Europe, and started discussions on adopting free-market systems within the Soviet Union in 1985 was Mikhail Gorbachev. Under his leadership, policies of glasnost (political openness) and perestroika (economic restructuring) were initiated. These reforms led to the end of the Soviet Union's control over Eastern European countries and ultimately to the dissolution of the Soviet Union itself by 1991. Gorbachev's introduction of greater freedoms and economic reforms marked a significant shift in Soviet Union policies during the Cold War era.