What will the US do if China invades Taiwan?

Beijing is rattling sabres like never before, sending three dozen military aircraft into Taiwan's air defence zone, the most it has ever deployed. Either the Chinese president Xi Zinping is taking advantage of Joe Biden's current political vulnerability to throw the gauntlet down or is actually building up to a full-scale invasion. We know he wants to do it at some point and may be running out of patience. Either way the Chinese leader is making calculations: if he does order an invasion will it be successful, can it be completed without too much bloodshed and, most importantly, what will Biden and the Pentagon do to stop him? It's a tricky one for Biden. The last thing he wants right now, or at any time in his presidency, is a war with China, even if it were to be restricted to a fight over Taiwan and not go further. But of course war isn't like that. It can't be compartmentalised. It's never neat and tidy. When the guns start firing, US versus China, there's no knowing what will happen next. Biden knows that, at least I hope he does. And Xi Zinping knows it too. He certainly wouldn't want things to escalate beyond his control. But he does want Taiwan back under the Beijing wing. The deployment of three dozen planes is a serious provocation but it's not war. What we don't know is what the Chinese president has in mind for the next, say, 12 months. I suspect what he will do is wait to see how Biden succeeds or fails in next year's mid-term elections, watch the Trump saga carefully to see if he makes a decision about standing in 2024 and then do somethng much worse than sending three dozen aircraft towards Taiwan. Something that looks like an invasion dress rehearsal just to see how the US reacts. If the US sends a couple of carrier strike groups to sail near Taiwan, Xi Zinping will get all angry about American intrusion but it will also help him in his strategic calculations. I fear Taiwan is doomed however many US aircraft carriers are in the region.