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The phrase "accordingly proceeding" is not correct and does not sound natural in written English.
It seems to be an attempt to convey a sense of following through with actions based on prior information, but it is not a standard expression.
Example: "We have reviewed the proposal and are accordingly proceeding with the next steps."
Alternatives: "therefore moving forward" or "thus continuing with".
Similar(60)
I shall accordingly proceed to assess the appellant's remaining pleas in law.
The history of race, then, is not like the history of, say, witches: a group that is shown not to exist and that accordingly proceeds to go away.
An experienced cook can pretty much suss out any potential problems by reading through the recipe and adjusting accordingly (say, proceeding cautiously with such generous amounts of butter, oil and cream).
Accordingly, I proceed to review the legislative history of the Act.
Accordingly we proceed to discuss the neural underpinnings of imitation and other mechanisms important for cultural learning: learning biases, mental state attribution, and reinforcement learning.
This place seemed to Xerxes a convenient spot for reviewing and numbering his soldiers; which things accordingly he proceeded to do.
Leaving the Pasitigris, accordingly, they proceeded to Persepolis, the capital of Persia, a march of twenty-four days.
Accordingly, he proceeds in all areas of inquiry in the manner of a modern-day natural scientist, who takes it for granted that progress follows the assiduous application of a well-trained mind and so, when presented with a problem, simply goes to work.
But with the market ten times its normal size, the algorithm adjusted accordingly and proceeded to complete its task in just nineteen minutes, sending the Dow into free fall.
45 Accordingly, we proceeded in a hierarchical manner.
Accordingly, we proceeded with these constructs to evaluate the efficiency of this screening system in CHO cells.
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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