What is the meaning of “do not act/do not engage” mean in Islam?

The meaning of “do not act/do not engage” is generally one of prohibition, and the meaning of “act/engage” is generally one of command as they both are in an imperative form. The prohibited acts are few in Islam and are therefore easy to stay away from. The test of staying clear of certain foods was the first test given to our father Adam and our mother Eve. The eating of the forbidden fruit was the first act of transgression against God as the Qur’an makes clear:

O Adam! Dwell you and your wife in the Garden and eat from what you desire, but do not come near this tree lest you become wrong-doers. Then Satan whispered to them that he might manifest unto them that which was hidden from them of their shame, and he said: Your Lord forbade you from this tree only lest you should become angels or become of the immortals. And he swore to them (saying): Indeed I am a sincere adviser unto you. Thus did he lead them on with guile. And when they tasted of the tree their shame was manifest to them and they began to hide (by heaping) on themselves some of the leaves of the Garden. And their Lord called them, (saying): Did I not forbid you from that tree and tell you: Indeed Satan is an open enemy to you?

These verses elucidate the extent of Divine mercy as God forbade Adam and Even to eat from only one tree and made all the others permissible for them. Likewise out of His infinite mercy God has made the prohibited things few in number in order to facilitate our obedience to Him. “O mankind! Eat of that which is lawful and wholesome in the earth, and follow not the footsteps of the devil. Indeed he is an open enemy for you.” Therefore the entire universe is the table of God created for man to benefit from in order for us to worship Him. The task of worshiping God has also been made easy by Him indicating for us the few things made prohibited. God has also promised forgiveness for those who fall into the prohibited and then turn to Him in sincere repentance. The Messenger of God said, “Leave to be that which I have brought to you as those before you were destroyed by their excessive questions and quarrels with their prophets. If I command you to do something then strive to obey as much as is possible, and if I forbid you from something then leave it alone.”
May God guide us to His obedience and our final prayer is all praise is due to God.