Let's take a look at the explanation by English native speakers about the difference. for just FYI.
行動:無意識的な動作と意識的な動作までを含む人の動作。action.
行動 : the movement of someone if it be unconscious or intentional.
動作:身体的な運動やその作用。movement.
Physical movement of it and the effect, movement.
地震の際には、落ち着いて適切な行動をとって身体の安全を確保しましょう。
不注意な行動が大きな危険を招きます。
Place yourself to security area, with with due composure in a case
of the earthquake. Your careless action could put you in danger.
ダンサーが舞台に登場して、野生の猿のような不思議な動作をしてみせた。
彼は店員としてのトレーニングが未熟で、まだ店頭での動作がぎこちない。
The dancer acted with strange movement of a wild ape while he is on the stage. He is still inexperienced in training, so his movement on the stage is awkward.
So that, whereas 行動 has broader sense of action, 動作 is more centered on the very motion/movement by someone/something.