Can I Install Windows 7 (64 bit)?

I currently have Windows 7 32 bit Installed on my Sony Vaio VGN-NR38S. I upgraded from Windows Vista 32 bit (already installed when the machine was bought from Costco). So I installed Windows 7 32 bit. But when going on CMD and typing in system info, it came up with my processor being an x64 Family 6 Model 15 Stepping 13 Genuine Intel ~2000 Mhz. I know that x86 is 32 bit and x64 is 64 bit. Does this mean that my computer is capable of running the 64 bit version of Windows 7? Thanks in advance.