According to Newton's third law, every force is accompanied by an equal and opposite force. How can a movement ever take place?

The force of action and reaction cannot cancel each other.

Action and reaction though equal and opposite forces always act on two different bodies and cannot cancel each other. If they acted on the same body, the resultant force would be zero and there could never be accelerated motion.

Every force is complied  by equal and opposite force, but these forces acts on two different bodies that results a movement.

Hence the correct option is (2).