Sorry, what? You seem to be confused.Not really... the military was being reduced in size after Regan's defeat of the Soviets...
Reagan didn't defeat anything. Gorbachev decided that starving his people in order to afford a nuclear program of that magnitude wasn't a great choice and initiated Perestroika. The economic reforms really went into overdrive in 1986 after Chernobyl and in 1987 when he opened up the free market with the laws on state enterprise.
Unfortunately, his "planning" was a little short sighted, and instead of opening up the free market economy he wanted, it cause the economy to collapse due to the fact that it lacked both a true free market, or any sort of actual central soviet style planning.
Perestrioka inadvertantly lead to the detente, and the end of the cold war.
Reagan didn't do much besides continuing to crank out US Nukes and waste tax payers money with Reaganomics.