Xに従って(従い) as “following X, in accordance with X”
The verb 従う (したがう/shitagau), which translates to “to abide, to obey, to follow, to accompany,” can be conjugated into its Pre-ます-Form (従い), or more commonly, its て-Form (従って), and placed after a NOUN word or VERB word in its Dictionary Form, X, along with the particle に to serve the grammatical function of “in accordance with X, following X.”
The usage of the Pre-ます-Form, 従い, is considered to be more formal and is usually used in written language, while the て-Form, 従って, can be used in both spoken and written language. Addtionally, the standalone phrasing of 従って can be used at the very beginning of a sentence without the particle に and a NOUN/VERB word to simply mean “therefore, accordingly, etc.,” in which it essentially performs the same grammatical function here as it refers to the context of the previous sentence as opposed to a particular NOUN/VERB word.
When this grammar pattern is used with VERB words, the VERB word used must be in its Dictionary Form, and the verb action overall should represent a continuous action as opposed to a momentary one.
Yakusoku ni shitagatte tabacco o suuno o yameta.
(“I stopped smoking in accordance with the promise I made.”)
Minna no kettei ni shitagatte, project o yarinaoshita.
(“Following the decision we made together, we redid the entire project.”)
Atama no itami ga tsuyoku naru ni shitagatte, shiken ni shuuchuu dekinai koto ni natta.
(“Following my headache getting worse and worse, I wasn’t able to concentrate on the test.”)