Apparently there is a Japanese word for
Moving forward taking the good things with you but leaving the bad things behind.
Would any of you know what it is?
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Someone asked almost the same question in Japanese here. The people that answered it there couldn't come up with any any proverbs or 四字熟語 that said that exactly, but the closest was 諦（あきら）めは心（こころ）の養生（ようせい）, which kind of means 'don't worry about the things you can't change'.