Let △A0B0C0 be an equilateral triangle with area 1, and let A1, B1, C1 be the midpoints of A0B0, B0C0, and C0A0, respectively. Furthermore, set A2, B2, C2 as the midpoints of segments A0A1, B0B1, and C0C1 respectively. For n≥1, A2n+1 is recursively defined as the midpoint of A2nA2n−1, and A2n+2 is recursively defined as the midpoint of A2n+1A2n−1. Recursively define Bn and Cn the same way. Compute the value of limn→∞[AnBnCn], where [AnBnCn] denotes the area of triangle △AnBnCn.