Idioms for keeping the big picture in mind while picking out the details

At least in the US, you could say don't miss the forest for the trees.

From Merriam-Webster's definition of miss the forest for the trees:

US
: to not understand or appreciate a larger situation, problem, etc., because one is considering only a few parts of it

In other words, don't focus so much on a detail that you lose track of the overall issue.

How about separate the wheat from the chaff? From Lexico:

separate (or sort) the wheat from the chaff: Distinguish valuable people or things from worthless ones.

One could interpret this to mean "from the big picture -- wheat and chaff -- 'cherry-pick' what is valuable -- the wheat."