In my study of Advaita Vedanta, I have come across many references to the point that one is not the doer of any action. See for example these two verses
धर्माधर्मौ सुखं दुखं मानसानि न ते विभो।
न कर्तासि न भोक्तासि मुक्त एवासि सर्वदा॥६॥
Righteousness, unrighteousness, pleasure and pain are connected with the mind and not with the all-pervading you. You are neither the doer nor the reaper of the actions, so you are always almost free.॥6॥
प्रकृते: क्रियमाणानि गुणै: कर्माणि सर्वश: |
अहङ्कारविमूढात्मा कर्ताहमिति मन्यते || Chapter 3, verse 27||
A egotist, under the influence of the three modes of material nature-Rajas, Sattva and Tamas, thinks himself to be the doer of activities, which are in actuality carried out by nature.
Now if I am not the doer and reaper of any action what's the significance of law of karma? Lord Krishna says what is happening with us is the result of our past actions.
So, shouldn't we be taking responsibility of what we are doing instead of saying that we are not the doer?
Here's what Vasistha has to say about people who think they are not the doer of any actions in Yog Vasistha:
He who thinks of going to heaven or hell by the will of the Maker is also a slave to destiny and is no better than a beast.28 The man of a noble mind who is employed in acts of goodness, breaks off from the errors of the world like a lion from its cage.29 Those who vainly imagine themselves to be led about by some supernatural power, and so slight their necessary duties, are to be shunned at a distance as the mean and base.
(Yog Vasistha, Part 2, chapter 6)
But again in later Yog Vasistha, I have found Vasistha saying that we not the doer of actions we perform.
At this point I am totally puzzled as what to do. At one point they all are saying that I am not the doer and at other point they are saying I am the doer. Am I the doer of my actions or not?