You'll have to remind me of the deal. Gorbachev's reforms inside the USSR - what did Reagan give in return for those that benefited Gorby? Nothing.it was time to try to make a deal
Do you refer to arms limitation deals? Certainly, Reagan's commitment to building militarily could not be matched by the Soviet economy - because, of course, it was already collapsing from its own interior contradictions. Gorbachev recognized the essential need to scale back the arms race so that he could rebuild the USSR economic structure.
In 1988 it was Gorbachev who announced the amazing conversion of thinking; the freedom of nations to choose their own leadership and the reduction/removal of Soviet troops in the "socialist republics". He intended to encourage a new, more liberal, association of "states" (so to speak) that would reinvigorate the CCCP economy. Instead he got the disintegration of the Union. That is what had nothing to do with Reagan (or the USA).
Gorbachev won a Nobel Peace Prize. But he never did "tear down this wall". That was the result of East German civilian pressure and the weakness of the regime to which Gorby had turned over the responsibility. They had to decide what to do and in the end they just couldn't become mass killers. It was the unavoidable result of Gorbachev's unintended "freedom".
From a historical perspective, it's wrong to give Reagan credit for the fall of the USSR. It's right to give him whatever credit results from not simply caving in to anti-militaristic doves in the USA.