your statement are false. that's why he is the GIFT in us. he do the work. don't make false accretion on the scriptures. #1. Eph 2:10 is stating he called and saved us for his purpose. that why he came in Spirit on Pentecost. we're the Spirit hands and feet that he work through.
Now your Matthew 25:31. the apostle Paul is saying exacting what the Lord Jesus is saying. Listen, 1 Corinthians 13:1 "Though I speak with the tongues of men and of angels, and have not charity, I am become as sounding brass, or a tinkling cymbal”. what the apostle is saying, if I don’t have GOD, the only true God the Holy Spirit, he’s NOTHING.. Yes, God, Charity is Love, and God is Love. It’s GOD, the Holy Spirit in you who do the works. This is exactly what the apostle James was saying in Chapter 2 of his book. Listen, James 2:1 "My brethren, have not the faith of our Lord Jesus Christ, the Lord of glory, with respect of persons”. see, if God dwells in you a sister or a brother need something the Spirit supply that need. it is the Christ in you will DO it.
See, these here in Matthew 25:31 are not saved, just like the demons in James book as he said about them.
Was it not you who pointed out that the demon are not SAVED. So are these, not having the LOVE of God/Christ in them. See, they didn’t have the Spirit in them or the LOVE of Christ in them they was NOT SAVED.. Hence NO works. if Christ be in you he will visit the sick, and those in prison.. ect. that's why those on the left was headed for destruction, because thwy was not his. Again the scripture, 2 Timothy 1:9 "Who
hath saved us, and
called us with an holy calling, not according to our works,
but according to his own purpose and grace, which was given us in Christ Jesus before the world began”. did you not read the fine print of the contract. "NOT I, but he in me, he doth the work"....

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Let me explain something to you. Many have misunderstood Paul and James on Faith and works. We will make it simple for you. No man or woman walk on a job site and start working, and then expect a pay check at the end of the week. No one must be hired first. The hiring is the SALVATION. If God is not in you then all your, YOUR work is in vain. just like thos in the Judgmen on the left. they was never hired/saved. As the pink panther said “exit stage LEFT”…. (smile).
Now, he said, for his own purpose and grace. Are we not in GRACE? Yes, so it’s not our work but his. As co-workers? Why, because he is in Spirit (see Acts chapter 2) and it's not us, but him. when Paul and Peter step in Rome, the Lord Jesus step in Rome. Are you getting this. See, we’re the HANDS and FEET of God/JESUS till he return. shame on you, this is basic christian teaching.
PS that the second ERROR, don't let it be another.
PCY.