Solved: Upgrading Laptop RAM (for integrated graphics)

Hi, I was thinking about upgrading the RAM in my laptop at some point. As it has integrated graphics (Intel HD 4000) it has no dedicated RAM but uses system RAM. Therefore I would like the fastest that I can possibly get (for gaming). The question is, what would be the fastest RAM I could put in this thing? At the moment it has 6GB of standard 1600MHz DDR3. Could I put some higher MHz RAM in there (and how high), and would it really be worth it considering the price/performance increase? Thanks in advance for any advice.

System Spec:

Model: HP Pavilion G6 Laptop
CPU: Intel i5-3210M (Integrated HD 4000 Graphics)
RAM: 6GB 1600MHz DDR3 RAM
SSD: Kingston SSDNow V300 (120GB)
HDD: 1TB Toshiba (5400 RPM)
OS: Windows 8 64-bit (soon to be 8.1, when I can get the darn thing to update!)