Great question, Frances!
You could do it in this order if you desired, but you never know the ONE time you're waiting on someone to get back to you for the CFC to be enough of a delay that recruiters could end the search because they found someone that fit the bill BEFORE your resume came through. Speed isn't always the key, but I like to get my application in as soon as possible in the event that a recruiter actually does have the time to go through it and will call me ASAP about a job.
On a side note related to your question, I NEVER write cover letters. Recruiter rarely (if ever) read them, so they are a complete waste of time. Also, if you have to change your resume for every job you're applying to, then that may be a good indicator that your job search is a bit too broad.
To give yourself the best chance to get a job that you're GREAT at, you generally shouldn't have more than one or two versions of your resume. If you find yourself changing your resume for each job, then I would re-evaluate the focus of your job search completely TBH.
Hope that's clear and helps, and if you have any more questions, please ask!
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