Recently, reinforcement learning (RL) has been applied to task-oriented dialogue systems by using latent actions to solve shortcomings of supervised learning (SL). In this paper, we propose a multi-domain task-oriented dialogue system, called Dialogue System with Optimizing a Recurrent Action Policy using Efficient Context (DORA), that uses SL, with subsequently applied RL to optimize dialogue systems using a recurrent dialogue policy. This dialogue policy recurrently generates explicit system actions as a both word-level and high-level policy. As a result, DORA is clearly optimized during both SL and RL steps by using an explicit system action policy that considers an efficient context instead of the entire dialogue history. The system actions are both interpretable and controllable, whereas the latent actions are not. DORA improved the success rate by 6.6 points on MultiWOZ 2.0 and by 10.9 points on MultiWOZ 2.1.