Adam sinned because he wanted to. God provided all the reasons, including Adam's nature, that Adam freely responded to.
Let's unpack what you just said:
Adam sinned because he wanted to.
I wouldn't say he wanted to, but I will say that he did choose to. There are choices we make in life that are out necessity, not out of desire. We can address that more if you wish.
God provided all the reasons
This is where this gets interesting ... (I certainly hope you can provide answers to "how" these "reasons" worked to bring about Adam's decision to sin.
Please remember, what you are defending is that because God decreed, ordained, and or predetermined that Adam would sin in the Garden of Eden, God HAD TO therefore "provide reasons" limit Adam's choice to be the one choice that aligned with the predetermined plan of God.
You do understand that Adam did NOT have a sin nature. Adam's nature was neutral. Something had to cause Adam to make the decision to sin.
You have just suggested with the preceding words that God provided the reasons that caused Adam to fulfill the predetermined decree of God.
This then is what needs to be reconciled:
Because God not only had foreknowledge of the sin of Adam, but also predetermined the outcome of Adam's choice, any and all "reasons" God "provided" which aided in the decision making process must be considered as coercion.
Yes, Adam made a choice, but that choice was was caused by circumstances deliberately placed in Adam's timeline to bring about a particular result; which as the WCF clearly states was predetermined by God. Hence, Adam effectively had no actual choice at all.