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"methodical thinking" is a correct and usable phrase in written English.
It can be used to describe when someone uses a systematic approach to solve a problem or come up with an answer. For example, "I used methodical thinking to figure out the answer to the difficult math problem."
Exact(3)
All in all, a good, solid pick consistent with the well-reasoned and methodical thinking often ascribed to Mr. Romney.
"The skills to succeed are methodical thinking and the willingness to work.
What got me was not only the methodical thinking behind the argument but also the fact that music, to this child, was a real, tangible thing.
Similar(57)
I am used to being methodical and thinking: 'If I do this then I will play well.' This is different.
We're all really excited about it, but I don't see very many people working in a diligent, methodical way on thinking through the implications.
"It would create upheaval, really chaos at a time when the county needs stability and methodical, intelligent thinking," said Judith A. Jacobs of Woodbury, the legislature's presiding Democrat.
[P1, female, 83 years] …it's a different mentality from ours… our way of thinking is methodical, rational and rigorous (Cartesian)… the young have a digital mind.
In a way, this is no less methodical or inventive than the manner of thinking that led Franklin to his electrical experiments or his conjectures about the Gulf Stream.
He is tasting, thinking and cataloging things in a methodical way all the time.
Under Thinking Patterns, they wrote, "The rounded arch formation of your m's and n's indicate your methodical, logical thinking," and, "The wedge formations in your m's and n's are a strong indication of your investigative thinking process".
Under Thinking Patterns, they wrote, "The rounded arch formation of your m's and n's indicate your methodical, logical thinking," and, "The wedge formations in your m's and n's are a strong indication of your investigative thinking process".
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com