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After the naniwa 5k try the coticule with water only, if it works that's perfect.
Depending on the coticule you have it could happen that it works better with some very light slurry.

I regularly use a combination stone king 1/6k, then the coticule or some other finisher. I find the 6k effective to clean the scrape pattern from 1k and better (finer) to prepare for the coticule...