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Hello and thank you for you question,Can you keep it running if you give it a little gas while stopping?
The most common cause for the type of problem you are having is in most cases is caused by a dirty and or failing IAC ( idle air control ) solenoid providing there are no engine vacuum leaks. Start first with removing the IAC from the throttle body and give it a good cleaning as well as the bore it sets in and see if that will resolve your problem. I have enclosed the location in the diagram below. Copy and paste the link to your browser to open and view it.https://dl.dropboxusercontent.com/u/104923897/IAC%20Nov%2010.pdf