Acts 3:1-4:4

In the same way that it was not because of a calculation or strategy of his own divising that Peter "raised his voice" to preach in Acts 2, but Peter was responding to what God done, because God "has poured forth this which you both see and hear" (Ac 2:33), so Peter did not set up a platform for his sermon in Acts 3:11, but denied anything about the healing  of "the man who had been lame from his mother's womb" (3:2) to be due to "our own power or piety" (3:12), when the man began walking and leaping and praising God and clinging to Peter and John,  and caused a crowd to come to the portico of Solomon (3:9,11).  Luke is giving a distinct flavor to the initial growth of the movement, that it was not originating in a human push.  But Peter and John certainly do things here in Acts 3!

The combination of God's working and man's actions is thus not a problem for Luke: here in the healing, God's power is used by Peter, and Peter does nothing by his own power or piety.  But that is just one way in which Luke describes the working of God in events. In the sermon of our current chapter, Peter gets very bold, once again, in assigning sinful actions and responsibility for them to men: "you disowned the Holy and Righteous One and asked for a murderer ..." (3:14).   But when explaining that further, Peter says that "you acted in ignorance, just as your rulers did also" (3:17).  (Now you have to know your Old Testament Levitical laws to know that acting in ignorance was no "excuse").   Therefore Peter is very proper to say both that God "has thus fulfilled" ... "the things ... announced beforehand by the mouth of all the prophets, that His Christ would suffer" (3:19), and to tell them "therefore repent and return, so that your sins may be wiped away" ... including the very sins he has just mentioned (3:19).

So, here we have an example, first, of God working powerfully in a healing, and second, of Peter describing God working to fulfill prior things announced, in the sins done in ignorance mentioned in 3:13-15.  

Next, in 3:19-20, Peter exhorts them to do something for the purpose of God causing something, three things actually, to come about.  The people were to "repent and return so that [1] your sins may be wiped away, [2] in order that times of refreshing may come from the presence of the Lord, [3] and that He may send Jesus, the Christ appointed for you."  So does Peter have a doctrine that God and man have no interactivity?  No.