Is the Fed Can't Ease Because There Is Inflation?

There appears to be a lot of uncertain surrounding what may occur if the s m p prairie darks to new los. The fed cannot ease and the government cannot stimulate, as either action is inherently inflationry. Is there any historical precedent for easying or stimulating during an inflationary recession? If so, what was the impact? For example, would spending an infra structure actually exasperate inflation? I imagine such spending would pressure certain commodities, but am not ain it would have the same broad impact on demand as occurred with the covid time.