I accepted a job offer with one company and have an interview with another next week but don't want to hurt my chances

So, as the title states, I accepted a job offer with one joj for part-time work and heard back from another today and have an interview next week. Ideally, I'd like these jobs to be both part-time, but initially applied at full-time. Should I bring this up in the interview that now I have another job and am looking for part-time? I didn't know if be in this situation, and regardless, I'll have to share my availability at one time or another.

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