google-gemini/veo-3-nano-banana-gemini-api-quickstart ? reverse-engineered prompt

Build me a simple Next.js app that acts like a lightweight AI studio for Google Gemini models.

I want one clean page where I can switch between making images, editing images, combining multiple images into a new one, and generating short videos from text or an image. Use the Gemini API with Veo 3 for video, Imagen 4 for image generation, and Gemini 2.5 Flash Image for fast image editing and composition.

Make the experience feel easy to use, with a prompt box, model selection, image upload and drag and drop, and a result area that shows the generated image or video. After something is created, I want to be able to download it, move between modes without starting over, and trim videos right in the browser.

Please wire up the API routes so everything works end to end, and make the UI look polished and modern. If you need to check the latest Gemini docs online while building, go ahead.