There will be no need for a full analysis here, as it is clear that Matthew could not have relied on Mark, and that Luke may indeed have:

Matthew 4:23 And Jesus went about all Galilee, teaching in their synagogues, and preaching the gospel of the kingdom, and healing all manner of sickness and all manner of disease among the people. 24 And his fame went throughout all Syria: and they brought unto him all sick people that were taken with divers diseases and torments, and those which were possessed with devils, and those which were lunatic, and those that had the palsy; and he healed them. 25 And there followed him great multitudes of people from Galilee, and from Decapolis, and from Jerusalem, and from Judaea, and from beyond Jordan.

Mark 1:35 And in the morning, rising up a great while before day, he went out, and departed into a solitary place, and there prayed. 36 And Simon and they that were with him followed after him. 37 And when they had found him, they said unto him, All men seek for thee. 38 And he said unto them, Let us go into the next towns, that I may preach there also: for therefore came I forth. 39 And he preached in their synagogues throughout all Galilee, and cast out devils.

Luke 4:40 Now when the sun was setting, all they that had any sick with divers diseases brought them unto him; and he laid his hands on every one of them, and healed them. 41 And devils also came out of many, crying out, and saying, Thou art Christ the Son of God. And he rebuking them suffered them not to speak: for they knew that he was Christ. 42 And when it was day, he departed and went into a desert place: and the people sought him, and came unto him, and stayed him, that he should not depart from them. 43 And he said unto them, I must preach the kingdom of God to other cities also: for therefore am I sent. 44 And he preached in the synagogues of Galilee.

Neville [196] comments on the absurdity of the QM thesis here, which must suppose that Matthew chose Mark 1:39 as a "suitable summary statement on which to build" but when writing 4:23a was also influenced by Mark 6:6b. This requires either that he was "very familiar" with Mark's account as a whole (which begs the question) or that he "browsed well ahead" until he came to 6:6. In view of the compositional procedures we have briefly outlined in our hub essay, the latter is unlikely. Moreover the Greek word periago ("went") is used three times in Matthew and only once in Mark; it is just as well to argue that Mark's use was influenced by Matthew's use, or that in this parallel, Matt and Mark independently chose the best Greek word to translate an Aramaic one. The composition of the rest of the passage required Matthew to conflate elements of Mark 1:14-15 and 1:23-28, an unlikely compositional procedure for just one and a half verses in Matthew (4:23-24a); likewise, drawing from Mark 1:32-34 and 3:7-8 to compose Matt. 4:24b-25 AND Matt. 8:16.