To take' something is done only by the person/the agent. The person 'taking' is solely performing the action/is the sole agent. Usually it for something simple, like an object.
'I took the book.' 'I took a test.' 'I took a nap.' 'I took the ball and threw it.'
For 'advice' you can use 'take' or 'accept,' but it has a slightly different feel to it...'I will take your advice,' vs 'I will accept your advice.' To use 'take' emphasizes the choice or the agency of the invidual doing the taking.
'To accept' something is more like a dative case usage where the person 'accepting' is the recipient/is receiving something. It could be a physical object, like accepting a gift or it could be abstract like 'advice.' It involves two parties: the person giving and the person accepting. But, it can be used for abstract concepts, like:
'I accept my fate.' Here, the person is accepting their fate given to them by the universe, God, providence, etc. It expresses humility or humbleness. Whereas a similar expression emphasizes the individual agency/choice/free will:
'I took my fate into my own hands.'
For instances where both can be used, philosophically, 'to take' emphasizes individual agency whereas to 'accept' emphasizes humility or being acted upon by a greater force, etc. Analogous to 'free will' vs 'determinism.'