The Abstraction and Reasoning Corpus for Artificial General Intelligence (ARC-AGI) is a generative, few-shot fluid intelligence benchmark. Although humans effortlessly solve ARC-AGI, it remains extremely difficult for even the most advanced artificial intelligence systems. Inspired by methods for modelling human intelligence spanning neuroscience to psychology, we propose a cognitively inspired ARC-AGI solver. Our solver integrates System 1 intuitions with System 2 reasoning in an efficient and interpretable process using neurosymbolic methods based on Vector Symbolic Algebras (VSAs). Our solver works by object-centric program synthesis, leveraging VSAs to represent abstract objects, guide solution search, and enable sample-efficient neural learning. Preliminary results indicate success, with our solver scoring 10.8 percent on ARC-AGI-1-Train and 3.0 percent on ARC-AGI-1-Eval. Additionally, our solver performs well on simpler benchmarks, scoring 94.5 percent on Sort-of-ARC and 83.1 percent on 1D-ARC—the latter outperforming GPT-4 at a tiny fraction of the computational cost. Importantly, our approach is unique; we believe we are the first to apply VSAs to ARC-AGI and have developed one of the most cognitively plausible ARC-AGI solvers yet. Our code is available at: https://github.com/ijoffe/ARC-VSA-2025.