  We present high-precision measurements of elliptic, triangular, and
quadrangular flow $v_{2}$, $v_{3}$, and $v_{4}$, respectively, at midrapidity
($|\eta|<1.0$) for identified hadrons $\pi$, $p$, $K$, $\varphi$, $K_s$,
$\Lambda$ as a function of centrality and transverse momentum in Au+Au
collisions at the center-of-mass energy $\sqrt{s_{\rm NN}}=$ 200 GeV. We
observe similar $v_{n}$ trends between light and strange mesons which indicates
that the heavier strange quarks flow as strongly as the lighter up and down
quarks. The number-of-constituent-quark scaling for $v_{2}$, $v_{3}$, and
$v_{4}$ is found to hold within statistical uncertainty for 0-10$\%$, 10-40$\%$
and 40-80$\%$ collision centrality intervals. The results are compared to
several viscous hydrodynamic calculations with varying initial conditions, and
could serve as an additional constraint to the development of hydrodynamic
models.
