regex strsplit expression in R so it only applies once to the first occurrence of a specific character in each string?

I have a list filled with strings: string<- c("SPG_L_subgenual_ACC_R", "SPG_R_MTG_L_pole", "MTG_L_pole_CerebellumGM_L")

I need to split the strings so they appear like:

"SPG_L", "subgenual_ACC_R", "SPG_R", "MTG_L_pole", "MTG_L_pole", "CerebellumGM_L"

I tried using the following regex expression to split the strings:

str_split(string,'(?<=[[RL]|pole])_')

But this leads to:

"SPG_L", "subgenual""ACC_R", "SPG_R", "MTG_L", "pole", "MTG_L", "pole", "CerebellumGM_L"

How do I edit the regex expression so it splits each string element at the "_" after the first occurrence of "R", "L" unless the first occurrence of "R" or "L" is followed by "pole", then it splits the string element after the first occurrence of "pole" and only splits each string element once?