Sorry, you have made the fallacy of which i have spoken just above.
You try to apply the scientific method of "modern materialistic science" to this, and of course, you get this conclusion.

(IFF) you PLAN to do something (THEN) your PLAN must be CAUSED by some desire.

In this, you are assuming time is linear and that the cause is before the effect.
Neither assumption is correct, and will lead you to a faulty conclusion.
(further, to talk about free will, we must talk about the now, and how it can affect the future and the past)

Your WILL is a measure of your ability to PLAN.

I would say that your will is closer to your ability to desire.

Your WILL is a slave to your DESIRE.

This is patently not true.
You see, there is a spot, a silence before the storm, where you can make a change in outcome.
Just after the incident, and just before your emotional response.
Every yogi knows this spot and makes use of it to change their lives.
Of course, this is all in the realm of metaphysics... so it is denied by "modern materialistic physics"

Your WILL is not "free".

From where i stand, i can clearly see the effect of free will.