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"Nibbling" means take small bites out of or show cautious interest in a project or proposal

1. He sat and stared out the window while nibbling on a piece of cheese from the plate of cheese and crackers on a small table at his side.
2. He sat while nibbling a cookie
3. Jarrell took the glass, and sat there nibbling and sipping. 
4. Lying there nibbling chocolate with freinds feels so relaxing
The rat keep on nibbling at our cabinet.