the meaning to be conveyed is the quality of
being able to explore a situation with multiple viewpoints instead of just stuck with one way of exploring the problem
What word (or a few words) will convey this idea?
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Just as a quick answer 'open minded' comes to mind.
lateral thinking seems like the most obvious choice to me...
Able to think outside of the box, broadminded.
The first word that pops into my head is dynamic. You could describe someone as a dynamic problem-solver, a dynamic thinker, etc.
You might also describe such a person as perspicacious, perceptive or judicious.
A multitasker is someone who can work on many things at once; in some contexts, that may be the word you're looking for.
If you're looking for an idiom to describe this person, you might say she keeps all the balls in the air or fires on all cylinders.
"Broad perspective". Broad being the counterpoint to both "one" and "track" and perspective adding flexibility to the subject of "thinking"