Putin and Reagan never met. Where you get that idea?
There's a picture going around on the internet that supposedly shows Reagan greeting people on the street in Moscow (perhaps in Red Square) with Putin — who would have been a young KGB agent at the time — in the crowd.
I believe the picture has been debunked. At the time, Putin was posted to East Germany, probably steaming envelopes open, or some such.
There is a famous picture of Reagan in 88 walking through Red Square of a person who looks like a younger Putin, greeting Reagan