Final answer:
The next action would be to counsel the patient that 6-8 weeks of treatment is often needed before significant improvement is achieved.
Step-by-step explanation:
If the patient returns in three weeks and complains that the skin is not better after initiating therapy for acne vulgaris with doxycycline, the next action would be to counsel the patient that 6-8 weeks of treatment is often needed before significant improvement is achieved (option A).
It is important to educate the patient about the timeline for improvement with acne treatment and to manage their expectations. Discontinuing the doxycycline and initiating minocycline therapy (option B) or advising the patient that antibiotics are likely not effective for him and should not be continued (option C) would not be appropriate at this stage.
Adding a second agent such as trimethoprim-sulfamethoxazole (option D) may be considered if the acne does not improve after a few months of monotherapy or if the acne is severe, but it is not the next step in this scenario.