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Purchasing a new camera with high optical zoom, HQ or HD video, and very fast shutter speeds. Help? - small hd with optical

I want to buy a digital camera. It is most likely to point and shoot, but I'm open to a digital SLR camera and is not too expensive. Ideally, I would like the prices range between $ 200 and $ 400 I would be at least a 7x optical zoom (at least 5x), such as HD (720p - no need) to fill to 1080 or even video of the CA, and a fast shutter speed. I will use it mainly for travel with my family, including small children. I would also like for the concert from time to time as the family photo-op, etc. Please help me!