Reagan's tax cuts led to nothing but the deficit at the latter end of the 80's and the quick burning up of Volcker's economic recoveries which would have led to a stable economy in the years to come had Reagan not interfered. Volcker lowered inflation with his policies and ended the stagflation crisis. And though his policies that did this contributed to the recession that existed for a short period in the early 80's (a fact I think he believed would happen before it got better), they ensured that the situation turned around from this divit quickly and strongly to a stable and successful economy. Reagan just took credit and left Bush to take the blame for the deficit and economic troubles from his own policies when Reaganomics came to a head in the late 80's.
And his military policy did nothing to the Soviets that finally led to their collapse. The USSR was already in dire economic straits long before Reagan and couldn't keep up with the US in terms of military build up. And that was nothing to do with Reagan, but was the result of a combined international effort against the USSR for decades. The USSR also only collapsed because of years corruption eating away at the system, and even then there was no assurance that it was going to fall, and only finally did so after Gorbachev democratized the nation at a hastened pace which led to destability. Had he perhaps done that slower, the USSR would still exist today. So the fall of the Soviets was nothing to do with Reagan. It was to do with the entire free world, and that free world working against the Russians for roughly three decades, and decades of Presidents from both parties working against the Soviets. And the defining thing that led to the fall of the USSR was Gorbachev's own policies. You could have had any President go into office, from any party and the Soviets would have gone the coarse they did.