Right afterwards, I get a notification from my computer's action center saying that iTunes has stopped working properly
Fingers crossed, your Windows 7 will have been recording some additional information about those.
First, open your Action Center and expand "Maintenance". Click "View reliability history":

Once the reliability report has been generated, look for Critical events for iTunes generated at the time of the "iTunes has stopped working" messages. Doubleclick the name iTunes in the critical events. (Don't click View solution.)
For example, here's a screenshot of my system showing what to click. (I don't have any iTunes critical events at the moment, so I'm using an Oblivion event to illustrate what we need to do.)

You should see something that looks like the following screenshot (only for iTunes, not Oblivion):

Copy and paste the contents of the problem report into a reply here. For example:
Description
Faulting Application Path: C:\Program Files (x86)\Bethesda Softworks\Oblivion\Oblivion.exe
Problem signature
Problem Event Name: APPCRASH
Application Name: Oblivion.exe
Application Version: 1.2.0.416
Application Timestamp: 462392c7
Fault Module Name: Oblivion.exe
Fault Module Version: 1.2.0.416
Fault Module Timestamp: 462392c7
Exception Code: c0000005
Exception Offset: 000c9a80
OS Version: 6.1.7601.2.1.0.256.1
Locale ID: 2057
Additional Information 1: 27c8
Additional Information 2: 27c8ce5af7a07bedf550bd9c573901b3
Additional Information 3: e56e
Additional Information 4: e56e9cfaf3cd1084b6b4c016d12ce64c
Extra information about the problem
Bucket ID: 414526327