Vision Language Models (VLMs) have recently achieved significant progress in bridging visual perception and linguistic reasoning. Recently, OpenAI o3 model introduced a zoom-in search strategy that effectively elicits active perception capabilities in VLMs, improving downstream task performance. However, enabling VLMs to reason effectively over appropriate image regions remains a core challenge in GUI grounding, particularly under high-resolution inputs and complex multi-element visual interactions. In this work, we propose LASER, a self-evolving framework that progressively endows VLMs with multi-step perception capabilities, enabling precise coordinate prediction. Specifically, our approach integrate Monte Carlo quality estimation with Intersection-over-Union (IoU)-based region quality evaluation to jointly encourage both accuracy and diversity in constructing high-quality preference data. This combination explicitly guides the model to focus on instruction-relevant key regions while adaptively allocating reasoning steps based on task complexity. Comprehensive experiments on the ScreenSpot Pro and ScreenSpot-v2 benchmarks demonstrate consistent performance gains, validating the effectiveness of our method. Furthermore, when fine-tuned on GTA1-7B, LASER achieves a score of 55.7 on the ScreenSpot-Pro benchmark, establishing a new state-of-the-art (SoTA) among 7B-scale models.