US in liquidity trap?

I have re-read the FOMC statement. Its wording is somewhat contradictory and in some points is very similar to the set of conditions defining so-called liquidity trap. 

“To promote the ongoing economic recovery and to help ensure that inflation, over time, is at levels consistent with its mandate, the Committee decided today to keep the target range for the federal funds rate at 0 to 1/4 percent.” 

There are two statements in one sentence. The Federal Reserve has to keep the rate low in order to galvanize the economy. In turn, the economy did not show any reaction to the low rate during the past three years and is not expected to grow another two years:    

“The Committee currently anticipates that economic conditions--including low rates of resource utilization and a subdued outlook for inflation over the medium run--are likely to warrant exceptionally low levels for the federal funds rate at least through mid-2013.”  

 To keep inflation in the target range one needs to be flexible and to have an opportunity to react when inflation expectations alter.  The rate fixed between 0 and ¼ percent is not a medicine any more. It can not counteract inflation rise because it is fixed. It can not counteract liquidity trap because the rate can not be negative. Hence, the Federal Reserve should not mix economic growth and inflation in one pot. This statement is self-contradictory and reveals a trivial misunderstanding of economics.  

All in all, the Federal Reserve admits that it has failed to improve real economic growth by near-zero rates and by pumping money into banks through the QE mechanism. Moreover, the FOMC does not see any real improvement at a mid-term horizon. Considering the experience of Japan who has been struggling through a liquidity trap for decades one may suggest that the U.S. is already in the trap and all current efforts are worthless.