There's no period between worshiping Allah swt alone and being good towards your parents- it's one sentence.

The only difference is that Allah swt put the worship of Him before mentioning the dutifulness towards parents.

In the Arabic language, whatever you mention before another, it means it's a sequence. Why? because the origin of life and our existence is from Allah swt and our secondary origin is from our parents. 

Ibn Abbas says, the most important after Allah swt and Prophet Muhammad PBUH are our parents. 
Jibreel AS made a dua to which the Prophet PBUH said Ameen: "May his nose be rubbed in dust (disgraced), whoever reaches their parents in old age and still they did not be the cause of him or her entering paradise". Our parents are the greatest opportunity for us to attain paradise. 

If you want to be connected to Allah swt then it is through your parents. Lower the wing of humility out of mercy. Not respect, not kindness but mercy. Because Rahma has a deeper meaning. They are human and may make mistakes. We must not even make the sound "Oof" or speak in a harsh tone. Always choose the most beautiful words. 

CC: Lecture by Bilal Assad "My Lord have mercy on them as they brought me up when I was small" Quran 17:24 
Large Arabic calligraphy is "Al-Walidayn" (parents)
Small calligraphy throughout reads "Jannah" (heaven)

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