I'll toss in 2 cents worth.
The Fed in loud and overt discussion addresses inflation and economic growth. Greenspan, in earlier years, would occasionally mention another elephant in the living room, but that went out of vogue and is now something only addressed quietly.
The elephant is the national debt and its interest. The discussion of it evolved into phrases like "debt service is a not inconsiderable factor in the demand for liquidity from the debt market and has an impact on prevailing rates". Which was Greenspan-speak for . . . if we let rates go too high, the rolling over of US govt debt instruments takes place at higher cost and raises the deficit, which demands even more liquidity from the debt markets.
In this context, it is not at all lost on the Fed that there is some merit in having a floor, not a ceiling, on inflation. Inflation cheapens the value of the large liability on the books called The National Debt. If the debt's interest were merely serviced each year, inflation would "pay it down".
So, it's useful to keep in mind that the Fed certainly has a desired floor on the GDP number, but subtly, they have one on the CPI, too.