How long should I wait to follow up?

I had a phone interview on Oct 31 and did a writing assignment which I turned in on Nov 6.

He said he would get in touch with me soon about results and what to do next. He didn't give a deadline just a broad mention of next steps including another interview with manager and that he wanted to finish process quickly.

I haven't done writing assignments before so should I take this as a sign they've decided to go with another person or should I try to follow up (and if i follow up should I wait another week or just send an email this week)?

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