I would interpret the term CP to mean Closed Position in this instance; Counter-prom would usually be CPP.
Now for some history:
Alex Moore editions 1 to 5, 1936 - 1947, describing the feather danced straight down LOD, step 2 "LF forward, on same LOD, but body turned slightly towards wall". No mention of preparing... or side lead.
Henry Jacques, Modern Ballroom Dancing, 1st edition, 1944, step 2 "Forward Left foot, a medium length step, preparing to step outside partner on right side."
Alex Moore, 6th edition, 1951, step 2 "LF forward, preparing to step outside partner, L shoulder leading."
Of course the shoulder lead has of more recent years become a side lead but the basic idea is the same and the two parts of the description complement each other. The shoulder/side lead prepares for the next step to be taken in CBMP which is a vital part of the OP position.