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Lookup Activity try to write query that runs your SP. This way Lookup Activity can run your SP. Also, inside
Lookup Activity you will have SP option. Try that option as well if that suits for you.
I believe your API provides you some values in output json of activity which you want to pass to SP parameters. Write expressions to take API values and pass them to SP parameters in
Hope this helps. Please let me know if any further queries.
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