The number of $f$-electrons in the $+3$ oxidation state of gadolinium $(Z=64)$ is $x$ and in the $+2$ oxidation state of ytterbium $(Z=70)$ is $y$. The sum of $x$ and $y$ is:

Which of the following statements related to lanthanoids is incorrect?

Arrange the following metal complexes/compounds in the increasing order of spin-only magnetic moment. Presume all three are high-spin systems.
(Atomic numbers: $Ce = 58$,$Gd = 64$,and $Eu = 63$.)
$(a)$ $(NH_4)_2[Ce(NO_3)_6]$
$(b)$ $Gd(NO_3)_3$
$(c)$ $Eu(NO_3)_3$
Answer is:

The electronic configurations of bivalent europium and trivalent cerium are
(atomic number : $Xe=54, Ce=58, Eu=63$ )

Assertion : Magnetic moment of $Dy^{3+}$ is highest among lanthanoids.
Reason : Orbital motion contributes to the magnetic moment.

On which factors does the stability of an oxidation state in Lanthanoid elements depend?