refactor(代码重复): 抽取共享工具函数与 UI 组件，消除多处重复实现

Co-authored-by: Cursor <cursoragent@cursor.com>

src/lib/generators/random.ts

@@ -0,0 +1,7 @@
+export function randomInt(min: number, max: number): number {
+  return Math.floor(Math.random() * (max - min + 1)) + min;
+}
+
+export function randomPick<T>(arr: readonly T[]): T {
+  return arr[Math.floor(Math.random() * arr.length)];
+}