I agree with both the fine answers already given but would just like to compliment you on your advanced grasp of the nuance here! You were "right on the money" when you differentiated between possibility and ability when choosing the word "could" rather than "can."
I also want to add an American usage note in regards to using "could" as simple past tense form of "can." Here it is: Americans tend to avoid using "could" to describe "ability" In the past tense.
For example, you WERE ABLE to interpret that title yourself. Do you see how I spoke of that past ability? Another common verb for past ability is "managed": You MANAGED to interpret that sentence for yourself. In common usage here, we are not likely to say, "You COULD interpret that title yourself" in speaking in past tense of your ability...probably because "could" is so full of the connotation of current/future possibility!
So, you may get an argument about this from some grammar teachers, but all you have to do is listen to actual usage, and you will hear that "could" is almost out of use as past tense for can. (It is, however, commonly used for negative past tense, that is, for INABILITY...such as, "I couldn't sleep last night," but this is way, way more than you asked!)