The increasing use of Advanced Language Models (ALMs) in diverse sectors, particularly due to their impressive capability to generate top-tier content following linguistic instructions, forms the core of this investigation. This study probes into ALMs' deployment in electronic hardware design, with a specific emphasis on the synthesis and enhancement of Verilog programming. We introduce an innovative framework, crafted to assess and amplify ALMs' productivity in this niche. The methodology commences with the initial crafting of Verilog programming via ALMs, succeeded by a distinct dual-stage refinement protocol. The premier stage prioritizes augmenting the code's operational and linguistic precision, while the latter stage is dedicated to aligning the code with Power-Performance-Area (PPA) benchmarks, a pivotal component in proficient hardware design. This bifurcated strategy, merging error remediation with PPA enhancement, has yielded substantial upgrades in the caliber of ALM-created Verilog programming. Our framework achieves an 81.37% rate in linguistic accuracy and 62.0% in operational efficacy in programming synthesis, surpassing current leading-edge techniques, such as 73% in linguistic accuracy and 46% in operational efficacy. These findings illuminate ALMs' aptitude in tackling complex technical domains and signal a positive shift in the mechanization of hardware design operations.