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James 4:8

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 8 Draw near to God and he will draw near to you. Cleanse your hands, you sinners; and purify your hearts,2 you double minded. [James tells those in the churches who are still sinning to purify their hearts by drawing near to God; which occurs by persistently and patiently waiting on Him, listening and obeying what you hear the Lord command you.]

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2 Draw near to God... purify your hearts. More evidence that a pure heart is not only possible, but required. James is writing to those in the churches, still captive to sin. Notice he says draw near to God. God is not found in sect meetings. God is not found in reading scriptures.  You must go to him. You must wait on him — listen silently, with the humility of a sinner in need of his changing power — grace.
Wait, watch, listen, hear, obey... wait, watch, listen, hear, obey..... seek, listen, obey. You must endure to the end, when Christ brings salvation.
You must abide in him. And now, little children, abide in him; so that when he appears, we may have confidence and not be ashamed before him at his coming. 1 John 2:28

Paul speaks of faith as: being obedient to the leading of the Spirit. See Footnotes 3 and 4 to Gal 3:24-25. Such faith can definitely purify the heart.