Dominant strategy for variant on “subtracting the square” game

Question

I was reading about the “subtract a square” game at https://en.m.wikipedia.org/wiki/Subtract_a_square , and I was thinking about potential variations on the concept. Under this variation, two players would begin play with a number of tokens between them. The two players would take turns subtracting a nonzero number of tokens equal to the sum of the a^2 and b^2 terms of a Pythagorean triple (two square numbers that equal a third square number when summed). If no Pythagorean triple can be subtracted from the pile, the players may subtract a single square number. The last player to remove tokens from the pile wins. I was wondering if there were a dominant strategy for a variant like this.