Could with two meanings refering to the past and to the present. How to choose?

[nivi_vi_vi]

Here it is the issue
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I can see that

Could can refer 1) Present 2) Past
Could can mean 1) is able/was able 2) might choose to do something

What beats me is how to undersatnd when it is said about the present or the past.
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Example

I could take part in this course, but I didn't do it.


I am sure that a native speaker sees "could" as - I might choose to take part...... Hence the second part of the sentence should be changed to the present.

However, what hinders us to see another meaning here? where "could" would mean - was able to - I was able to take part in this course but I did't do it.

I could take part in this course, but I didn't do it. = I was able to take part in this course, but I didn't do it.