Generative Search Engines (GSEs) have reshaped information retrieval, and Generative Engine Optimization (GEO) emerges to improve the content visibility in GSEs’ responses. Previous methods mainly rely on empirical strategies or query-dependent preferences of GSEs for content optimization. However, they remain limited in effectiveness as they overlook the latent user search demands in queries that drive content retrieval and response generation of GSEs. To address this, we propose Mind Reader, a novel GEO method to effectively improve the content visibility within the generated responses of GSEs through content optimization guided by the extracted latent demands of user search. Specifically, we propose a decomposition-recombination query augmentation module, which enriches the query with latent semantic information by decomposing it into diverse perspectives, capturing underlying semantic information, and recombining them into variants to support subsequent optimization. Then, we propose a reasoning coverage content optimization module. By optimizing content to cover critical reasoning information of GSEs, we align the content with the user search demands, effectively improving the content visibility. Extensive experiments on widely used GEO-Bench and our proposed PC-GEO show that our method significantly outperforms baselines and effectively improves content visibility (with up to 2.44x objective metrics and 1.23x subjective metrics on average).