Estimating ground state energy of $n$-qubit $2$-local Hamiltonian $H$ with known coefficients

Suppose we have an $n$-qubit $2$-local Hamiltonian $H$ with known coefficients. The eigenvalues of $H$ lie in $[0,1)$ and can all be written exactly with $[2 \log_2n]$ bits of precision. You would like to exactly determine thesmallest eigenvalue $\lambda_{\min}$ of H, corresponding to an unknown $n$-qubit eigenstate $|\psi_{\min}\rangle$. You are given (as aquantum state) an $n$-qubit state $|\psi\rangle$ that has a significant overlap with $|\psi_{\min}\rangle$: $\langle\psi||\psi_{\min}\rangle \ge 0.7$. Now please give a quantum algorithm with gate complexity poly($n$) that outputs $\lambda_{\min}$ exactly with probability $\ge \frac{2}{3}$

I know I should use phase estmating, but I have no idea about detail. Can someone give me some hint?