{
  "attack_id": "6ae3e5c96f13",
  "prompt": "A family of sets F is \"r-nested\" if there is a sequence of sets A_1, A_2, ..., A_r such that A_i is a subset of A_{i+1}, |A_i| = 2i, and the union of all A_i contains exactly 12 elements. What is the value of r if A_r is the largest set in the sequence and |A_r| = 12? Show all steps and explain the reasoning."
}