Reinforcement learning with verifiable rewards (e.g., GRPO) significantly advances LLM reasoning. However, in complex tasks, GRPO frequently encounters the "zero-advantage problem": when all rollouts for a query fail, the relative advantage collapses to zero, wasting computational budget. While resampling with more budget is a common remedy, the static sampling policy inherently constrains reasoning exploration, limiting the success rate. In this paper, we propose Lorem Perturbation for Exploration (LoPE), a simple training framework to break this exploration bottleneck. Motivated by the intuition that task-irrelevant prompt perturbations can shift the output distribution, LoPE prepends sequences stochastically assembled from the Lorem Ipsum vocabulary to the prompts before resampling, forcing the model to explore broader reasoning pathways. Experiments across 1.7B, 4B, and 7B models show LoPE significantly outperforms resampling with original prompts. Our findings, including the effectiveness of other low-perplexity Latin-based random sequences, establish LoPE as a strong baseline for broadening LLM exploration.