react/react-native ? reverse-engineered prompt

Build me a simple React Native app that works on both iPhone and Android and feels polished on each platform.

I want a clean starter app with a welcome screen, a few reusable components, basic navigation between screens, and a couple of simple interactions like tapping buttons and editing text. Make it use native UI controls where it makes sense, and make the layout responsive so it looks good on different screen sizes. If there are any current best practices or setup details I should follow, please look up the latest docs online.

Keep the code easy to understand, and include whatever is needed so I can run it locally and see changes quickly while I edit. If you can, add a small example feature that shows how to reuse the same React code across iOS and Android without changing much.