Computation of nearby cycles, monodromy action and action of $sl_{2}$ on $\operatorname{gr}(Ψ)$ for Picard-Lefshetz family

Question

Let $f: \mathbb{A}^{2} \rightarrow \mathbb{A}^{1}$ be a map that sends $(x,y)$ to $xy$. Let $U \hookrightarrow \mathbb{A}^{2}$ be the preimage $f^{-1}(\mathbb{A}^{2} \setminus \{0\})$ and $X:=f^{−1}(0)$. Consider the shifted constant sheaf $\mathbb{C}_{U}[2]$ on $U$. Let $\Psi(\mathbb{C}_{U}[2])$ denote the nearby cycles functor applied to $\mathbb{C}_{U}[2]$. It gives us a perverse sheaf on $X$.

My question is: how to compute this perverse sheaf on $X$ and the action of monodromy on it? Also if the action is unipotent then how to calculate the action of "Lefshetz" $sl_{2}$ on $\operatorname{gr}(\Psi(\mathbb{C}_{U}[2]))$?

Thanks!