If you want to call that a work, ok.
Jesus said that belief was a work and that it encompassed more than personal thoughts.
He never taught that he would cause people to work. Your statements are not really disputable so I don't intend to do that. You're right, we are led by the Spirit. But the typical "faith only" proponent will assert that evidence that we're saved is not because we of our own free will submit to the Spirit, but because the Spirit pushes us do the works we're created to walk in.
What usually goes hand in hand with this doctrine is that "saved" people were never saved in the first place if they do not produce fruit or work.
In other words, if we were EVER saved, we will do what God makes us do through the spirit. Yet the language is often of the sort of "irrefutable" language which doesn't say this at all and the pretext has to be read into it - the HOW it works being implied but not openly stated.
Permanent assurance combined with faith only says that a person who has turned away from God, is itself evidence that he was never saved in the first place. The only real evidence that exits in that case is that the person isn't at this moment obedient to God.
This also presumes that man has no free will and salvation therefore is a sort of programmatic result which had nothing to do with his own choices but what God has caused him and continues to cause him to do.
Yet, nowhere in scripture is the integrated explanation of such a thing ever presented to those preached the gospel either before or after their entrance into Christ.
The scriptures actually teach the opposite of this but you can take a few things out of context and say they "prove" that this is how it works.
If it were, then Peter on the day of Pentecost never would have commanded anyone do anything except think thoughts in their head and that they would begin to notice themselves doing things the Holy Spirit was telling them to do. By that logic, if a person went into a prostitute, they could just claim the Holy Spirit guided them to do that. "Well, I got saved and then I had the desire to find myself a bit of adult pleasure." Isn't God amazing?