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The phrase "critically determine" is correct and usable in written English.
You could use it in any context in which you need to express that you are carefully considering something in order to make a judgment. For example, "We must critically determine which of these approaches is most suitable for our project."
Exact(30)
Multiwalled carbon nanotube (MWCNT) length is suggested to critically determine their pulmonary toxicity.
Decisions made during a building's early design stages critically determine its environmental impact.
Selection of the coagulant type and dosages critically determine the success of as well as efficiency of treatment achieved.
Decisions made in the early design stages critically determine a building's life cycle environmental impacts and costs.
In the period of knowledge-based economies and societies, the level of scientific and technological capacities of nation states seems to critically determine their global status.
A good background in the nature of science will allow the student to critically determine the difference between good science and pseudoscience.
Similar(30)
It also critically determined what they did.
Vast aspects of human behavior are determined by our genes, but much of how that genetic material will be expressed is critically determined by the environment.
We devised a system in which the water content critically determines the stable self-assembly structures.
These results demonstrate that the presence of SOA vs. DOA effects can be critically determined by the identicality between targets.
Dendritic structure critically determines the electrical properties of neurons and, thereby, defines the fundamental process of input-to-output conversion.
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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