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You don’t need a new serial number. The Advantage Pack (aka 2012 AP) runs with your 2012 license. So, if you have a Network license, just point 2012 AP to your license server. If you have a Standalone license, enter your 2012 serial number at startup.
Use the same product key as 2012: 590D1
The 2012 AP will install in a folder named Softimage 2012.SAP.
For example: C:\Program Files\Autodesk\Softimage 2012.SAP.