# Filtering a doubly nested list

For some particular reasons I have a nested list, e.g.,

Dimensions[ourlist]={N,M,3}


where the third dimension includes 3 elements: the function, its first and second derivatives. So basically, each entry of the third dimension looks like this:

{ 1 , {1,1,1} ,{{1,2,3},{1,2,3},{1,2,3}} }

I can't figure out how to delete cases in this nested list (NxMx3) in which the norm of the gradient, i.e. the vector {1,1,1}, is larger than a threshold value. Any suggestion would be appreciated. Thank you!

One way is to use Pick:
ourlist = Table[{"f", RandomReal[1, 3], "f''"}, {2}, {5}]