Turning Turtles (Coin-Turning Game)

Turning Turtles is a coin-turning game on a row of coins numbered 1, 2, 3, ... A move chooses a coin showing HEADS at some position k, turns it to TAILS, and simultaneously turns over EXACTLY ONE other coin at a position j < k (to either face). The player who cannot move (all tails) loses. A standard result is that a single heads at position k is equivalent to a Nim heap of size k, and a position is the XOR (disjunctive sum) of its heads. If the only heads are at positions 3 and 6, does the player to move win or lose?