The symmetric-power compatibility conjecture for the graded Grothendieck-ring involution

Let $K_0(\operatorname{Var}_k^{\dim})$ be the graded Grothendieck ring of varieties, equipped with the symmetric-power operations $\operatorname{Sym}^m$ and the involution $\mathbb{D}$ that interchanges $\tau=[\operatorname{Spec}k]_1$ and $\mathbb{L}=[\mathbb{A}^1]_1$. Symmetric-power compatibility conjecture. For each $m\geq 0$, symmetric powers commute with the involution:

$$\operatorname{Sym}^m\circ\mathbb{D}=\mathbb{D}\circ\operatorname{Sym}^m.$$

The conjecture expresses the expected compatibility between the involution and the symmetric-power operations, motivated by the fact that the involution exchanges the basic degree-one classes $\tau$ and $\mathbb{L}$.