Stars rarely form in isolation, so it is critical to understand how the parsec-scale molecular cloud environment shapes the formation of individual dense cores at the sub-0.1 pc scale. To address the pathway to filament and core formation in clustered environments, we developed the CARMA Large Area Star Formation Survey, which spectrally imaged dense gas tracer lines across 800 square arcminutes of the Perseus and Serpens Molecular clouds with 7'' angular resolution. I will discuss the key results from initial papers. First, we found that filaments seen with Herschel show substructure in our high-resolution maps, and that several filaments show strong radial velocity gradients. I will compare the observed filament gradients with results from numerical simulations of filament formation from turbulent flows to support the idea that the observed filaments are self-gravitating and accreting material from an environment that is flattened at larger scales. Second, we found that the hierarchical complexity of dense gas structures, as measured by our new non-binary dendrogram code applied to our N2H+ J=1-0 data, correlates with the amount of star formation activity in different parts of the Perseus Molecular Cloud. Lastly, I will show how we can use dendrogram-identified structures in combination with high-resolution maps of centroid velocity and line-of-sight velocity dispersion to determine the line-of-sight depth of cloud regions. We found that Serpens Main and Barnard 1 are flattened (sheet-like) at parsec scales, and that all structures have a similar depth into the plane of the sky, on the order of 0.1-0.2 pc. All of these initial results imply that over-dense, sheet-like regions in molecular clouds fragment into filaments, and build up hierarchical structures on the pathway to forming dense cores.