(Reuters) -The number of Americans filing new applications for unemployment benefits ticked up in the latest week, but appeared to be steadying near a level consistent with a gradual cooling of the labor market that should set the stage for the Federal Reserve to kick off interest rate cuts next month. A slowdown in overall U.S. business activity this month as firms faced diminished ability to push through price increases added to the evidence that the economy is slowing and inflation is downshifting to a degree that should allow Fed officials to focus more attention on the job market. With a rate cut now broadly expected next month, interest rates on home loans have already begun dropping, and that helped fuel a larger-than-expected rebound in existing home sales last month.