The local Langlands correspondence for a connected reductive $p$-adic group $G$ partitions the set of equivalence classes of smooth irreducible representations of $G(F)$ into $L$-packets using equivalence classes of Langlands parameters. Vogan's geometric perspective gives us a moduli space of Langlands parameters, and the correspondence can be viewed as a relation between the set of equivalence classes of smooth irreducible representations of $G(F)$ and simple objects in the category of equivariant perverse sheaves on the moduli space of Langlands parameters that share a common infinitesimal parameter. This geometry gives us the notion of an ABV-packet, a set of smooth irreducible representations of $G(F)$, which conjecturally generalizes the notion of a local Arthur packet - a local Arthur packet is conjecturally an ABV-packet. In this talk, we will look at Langlands parameters coming from simple Arthur parameters in the case of $\mathrm{GL}_n.$ We will explore the geometry of the moduli space of Langlands parameters using an example. We will see work in progress towards proving that the local Arthur packet is the ABV-packet for this case.