How will Biden react if Putin launches nukes at Ukraine?

If Putin in desperation hits Ukraine with tactical nuclear weapons (still I believe a very remote possibility) how on earth will Joe Biden respond? He will have the almost impossible job of deciding whether to answer in kind (surely not), launch massive conventional strikes against Russian troops in Ukraine or even in Russia itself (the US military top dogs might well advise that) or just double up on sanctions to isolate Russia even more? The trouble is, using nukes would be such an enormous step, both for Putin and for the whole planet that a sanctions response would be seen everywhere, especially in Moscow, as weakness and an admission that deterrence had failed. But any form of military retaliation would lead to unpredictable consequences, even to the one thing the Cold War succeeded in preventing - nuclear exchanges between the US and Russia. Thus Armageddon for all of us. We had this in 1962 during the Cuban missile crisis when Nikita Krushchev, as Max Hastings has pointed out in his new book on the crisis, hastily stepped back when he realised the potential consequences of his reckless gamble - putting nuclear missiles on Cuba to threaten the US. But is Putin more reckless than Krushchev? Is Putin a bigger gambler knowing he has Biden to outsmart rather than John F Kennedy? There has to be a serious risk that Putin might go for the high stakes option because he might convince himself that Biden will do nothing except increase sanctions. But going nuclear would be an unbelievably dangerous move and Putin must know that. So Biden has to make clear to Putin, if he hasn't already done so, that if he launches a nuclear strike on Ukraine, the US WILL respond with a military attack and leave the targets and scale ambiguous, to make the Russian leader sweat. The White House is talking of catastrophic consequences in the event of a Russian nuclear attack. Catastrophic for Ukraine and for the world but will it be catstrophic for Putin and Russia? That's what Putin needs to be convinced about. Then he will leave the nuke option well alone.