Orbits of action of the split group of type $F_4$

Let the split group of type $ F_4$ act as the automorphism group of the split Albert algebra $ A$ . Consider the action of $ F_4\times \mathbb{G}_m$ on $ A$ , given by letting $ \mathbb{G}_m$ act by scalar multiplication.

Does this action have finitely many orbits? Are the stabilizers known? I am very new to $ F_4$ and I am slowly going through the basics, but a reference in this direction would greatly simplify my life.

Thank you.