It is possible that the passage that you are referring to in the gospel of Matthew is found in chapter 7, verses 15-17.  These verses say “Beware of false prophets, which come to you in sheep’s clothing, but inwardly they are ravening wolves. Ye shall know them by their fruits. Do men gather grapes of thorns, or figs of thistles? Even so every good tree bringeth forth good fruit; but a corrupt tree bringeth forth evil fruit.” These verses mean that true believers will demonstrate their faith by doing good things.  Unbelievers will demonstrate their lack of faith by doing sinful things.  So yes, faith is belief that results in good actions which in turn show the reality of a person’s faith.

You also referred to Psalm 46:10. This verse says, “Be still, and know that I am God: I will be exalted among the heathen, I will be exalted in the earth.” Another verse about waiting is Psalm 27:14, “Wait on the Lord: be of good courage, and he shall strengthen thine heart: wait, I say, on the Lord.”

Concerning whether to act or wait, let us consider Psalm 32:8. This verse says, “I will instruct thee and teach thee in the way which thou shalt go: I will guide thee with mine eye.” The Lord promises us in this verse that He will guide us with His eye.  In order for us to see where He is looking, we need to be close to Him.  How do we get close to Him?  By spending time with Him!  If we speak to Him through prayer and listen to Him through his Word, then we will get to know what pleases Him and what does not please Him.  A similar thought is found in Romans 12:1-2, “I beseech you therefore, brethren, by the mercies of God, that ye present your bodies a living sacrifice, holy, acceptable unto God, which is your reasonable service. And be not conformed to this world: but be ye transformed by the renewing of your mind, that ye may prove what is that good, and acceptable, and perfect, will of God.” Renewing our minds through the Word of God will give us wisdom to know God’s perfect will, whether He wants us to wait or to act.

Another principle is found in John 7:14-17, “But when it was now the midst of the feast Jesus went up into the temple, and began to teach. The Jews then were astonished, saying, How has this man become learned, having never been educated?” So Jesus answered them and said, My teaching is not Mine, but His who sent Me. If anyone is willing to do His will, he will know of the teaching, whether it is of God or whether I speak from Myself (NASB). The Jews were trying to figure out where the Lord received his teaching.  The Lord Jesus told them that if anyone is willing to DO His will, that the answer will be given to that person.  Applying this to your question, the Lord may not reveal WHAT His will is for you in a certain matter until you are genuinely willing to DO His will.

Not long before the Lord Jesus went to the cross, He said these words to His disciples in John 14:27, “Peace I leave with you, my peace I give unto you: not as the world giveth, give I unto you. Let not your heart be troubled, neither let it be afraid.” Peace is mentioned twice in this verse.  The peace that He left with us is found in Romans 5:1, “Therefore being justified by faith, we have peace with God through our Lord Jesus Christ.” Then He mentions that He gives us HIS peace.  We read of this in Colossians 3:16, “Let the peace of Christ rule in your hearts, to which indeed you were called in one body; and be thankful” (NASB). Our Lord and Savior Jesus Christ not only made it possible for us to have peace with God through His work on the cross for our sins.  He also wants us to let His peace rule our hearts.  This means that we need to wait for Him to give us peace about a decision before we act.  If you are unsure and troubled about a decision, then wait on the Lord.  However, when He gives you peace about a matter, and then confidently do what He wants you to do.  The Lord is with you and will guide you with all of the large and small decisions of your life.  (181.2)  (DJ)