Subconvex bound for $\text{GL(3)}\times \text{GL(2)}$ $L$-functions: $\text{GL(3)}$-spectral aspect

Let $\varphi$ be a Hecke-Maass cusp form for $\mathrm{S}\mathrm{L}(3,\mathbb{Z})$ with Langlands parameters $({\mathbf{t}}_i{)}_{i=1}^3$ and $f$ be a holomorphic or Hecke-Maass cusp form for $\mathrm{S}\mathrm{L}(2,\mathbb{Z})$. In this article, we prove the following subconvex bound $$L(\varphi \times f,1\mathrm{/}2){\ll }_{f,ϵ}{T}^{\frac{3}{2}-{\delta }_{\xi }+ϵ},{\delta }_{\xi }=\min \{\xi \mathrm{/}4,(1-2\xi )\mathrm{/}4\},$$ for the central value $L(\varphi \times f,1\mathrm{/}2)$ in the $\mathrm{G}\mathrm{L}(3)$-spectral aspect, where $({\mathbf{t}}_i{)}_{i=1}^3$ satisfies $$\mathrm{\mid }{\mathbf{t}}_3-{\mathbf{t}}_2\mathrm{\mid }\asymp T^{1-\xi },{\mathbf{t}}_i\asymp T,i=1,2,3,$$ with $\xi$ a real number such that $0<\xi <1\mathrm{/}2$.