'In Jenkins can I use both "Build after other projects are built" and "Build periodically" on a project

I want to kick off a build based on both "Build after other projects are built" and "Build periodically". I want it to execute daily at midnight which I can do with the cron schedule using build periodically. However I want it to execute only if one or more of four other projects have been built. Can I use both of these options and have it only execute if one or some of these projects have been built?



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