Psychological assessments commonly rely on rating-scale items, which require respondents to condense complex experiences into predefined categories. Although rich, unstructured text is often captured alongside these scales, it rarely contributes to measuring the target trait because it lacks direct mapping to the latent scale. We introduce the Information-Determined Scoring (IDS) framework, where large language models (LLMs) score free-text responses with simple prompts to generate candidate items that are co-calibrated with a baseline scale and retained based on the psychometric information they provide about the target trait. This marks a conceptual departure from traditional automated text scoring by prioritising information gain over fidelity to expert rubrics or human-annotated data. Using depression as a case study, we developed and tested the method in upper-secondary students (n = 693) and a matched synthetic dataset (n = 3,000). Across held-out test sets, augmenting a 19-item rating-scale measure with LLM-derived items yielded significant improvements in measurement precision and accuracy, and stronger convergent validity with an external suicidality measure throughout the adaptive test. In adaptive simulations, LLM-derived items contributed information equivalent to adding up to 6.3 and 16.0 rating-scale items in real and synthetic data, respectively. This enabled earlier high-precision measurement: after 10 items, 46.3% of respondents reached SE <= .3 under the strongest augmented test compared with 35.5% at baseline in real data, and 60.4% versus 34.7% in synthetic data. These findings illustrate how the IDS framework leverages unstructured text to enhance existing psychological measures, with applications in clinical health and beyond.