This debate has reached an impasse. We need a novel approach to _____ the current impasse.
What would be an idiomatic verb for the blank? Remove? destroy? resolve? bring us out of? bring the debate our of? ...
One typically breaks an impasse, as in these two sample sentences found in Merriam Webster:
// But Gilbert’s request for his mother to go out and get him a can of coke on the night of the murder in 2015 broke the impasse among the jurors.
— Fox News, "Jurors in father killer trial over cut off allowance say a can of coke was 'aha moment' that helped to find him guilty," 30 June 2019
// Nevertheless, facilitating dialogue may be insufficient to break the impasse.
— Adem K Abebe, Quartz Africa, "In Sudan, the African Union reminds us it still has a key role in tackling the continent’s crises," 7 June 2019
This is supported by the Google Ngram Viewer (thanks @JasonBassford for reminding me), if you conduct a search for
*_VERB the impasse you see break is used about twice as often as resolve (even when counting the declensions broke and resolving):