The Range Avoidance (Avoid) problem is defined as follows: given an expanding circuit $C:[N] \rightarrow [2N]$, find a $y \in [2N]$ that is not in the range of C. Intuitively C maps N pigeons to 2N pigeonholes, and we are looking for an empty pigeonhole. The exact complexity of Avoid has attracted a lot of attention in theoretical computer science in recent years due to its close connection to explicit constructions: the task of constructing many important combinatorial objects such as Ramsey graphs, rigid matrices and two-source extractors reduces to that of solving Avoid. We show that Avoid is provably NOT NP-hard (assuming that the Polynomial Hierarchy does not collapse). More generally any decision problem efficiently reducible to Avoid is contained in AM intersect coAM. Underlying our proof is an Arthur-Merlin type algorithm that solves Avoid and a novel AM protocol for upper bounding the size of the image of any given circuit. This talk is based on a recent paper (https://eccc.weizmann.ac.il/report/2025/210), joint with Surendra Ghentiyala and Noah Stephens-Davidowitz, to appear in STOC 2026.