Writing is hard okey

A few days ago I had an interview with a committee of two whole people. I did not get the job for reasons logical to everybody. However, the "CEO" of the project told me to apply for a similar position but way more challenging. For this i need to write another application letter.

I'm a bit lost here because I do not know should I write it like the interview never happened? I'm more or less sure the same people will read it who did previously.

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