by putting nuke silos in Turkey. That's why Russia retaliated by building them in Cuba. That's the bit that most people in the US like to try to forget. Both installations were dismantled and the Mexican standoff continued.
What I'll never forget is the eerie silence over several days. I was in school and no one spoke, not even in the cafeteria. We were all locked inside our heads, all veterans of "duck and cover" who had been terrified since kindergarten over what a bunch of stupid men in governments could and probably would do to us all but afraid to say anything out loud, making it more real.
Will Putin toss a nuke? It's hard to know for sure, but my guess is that he's fighting all his generals and intelligence people over it. For one thing, Ukraine hasn't given them an appropriate battlefield target, they'd have to hit a city. For another, even if a small yield bomb were deployed against some kind of military target, the act would cost Russia the support of everyone but N. Korea, which isn't much support, at all. And that doesn't even take into account a NATO response with up to date systems, not just the 25 year olds stuff we've given to Ukraine.
As for being backed into a corner, he's not. He still thinks he's an Emperor, his position unassailable and all setbacks only remporary. He will likely think that until he's halfway to the ground after being pitched out of a window.