On graphs in which neighborhoods of vertices are strongly regular with parameters (85,14,3,2) or (325,54,3,10)

J. Koolen posed the problem of studying distance regular graphs in which neighborhoods of vertices are strongly regular graphs with nonprincipal eigenvalue at most $t$ for a given positive integer$t$. This problem was solved earlier for $t=3$. In the case $t=4$, a reduction to graphs in which neighborhoods of vertices have parameters (352,26,0,2), (352,36,0,4), (243,22,1,2), (729,112,1,20), (204,28,2,4), (232,33,2,5), (676,108,2,20), (85,14,3,2), or (325,54,3,10) was obtained. In the present paper, we prove that a distance regular graph in which neighborhoods of vertices are strongly regular with parameters $(85,14,3,2)$ or $(325,54,3,10)$ has intersection array $\{85,70,1;1,14,85\}$ or $\{325,270,1;1,54,325\}$. In addition, we find possible automorphisms of a graph with intersection array $\{85,70,1;1,14,85\}$.