  We propose a novel class of Nesterov's stochastic accelerated
forward-reflected-based methods with variance reduction to solve root-finding
problems under $\frac{1}{L}$-co-coerciveness. Our algorithm is single-loop and
leverages a new family of unbiased variance-reduced estimators specifically
designed for root-finding problems. It achieves both $\mathcal{O}(L^2/k^2)$ and
$o(1/k^2)$-last-iterate convergence rates in terms of expected operator squared
norm, where $k$ denotes the iteration counter. We instantiate our framework for
two prominent estimators: SVRG and SAGA. By an appropriate choice of
parameters, both variants attain an oracle complexity of $\mathcal{O}( n +
Ln^{2/3}\epsilon^{-1})$ to reach an $\epsilon$-solution, where $n$ represents
the number of summands in the finite-sum operator. Furthermore, under
$\mu$-strong quasi-monotonicity, our method achieves a linear convergence rate
and an oracle complexity of $\mathcal{O}(n+ \kappa
n^{2/3}\log(\epsilon^{-1}))$, where $\kappa := \frac{L}{\mu}$. We extend our
approach to solve a class of finite-sum monotone inclusions, demonstrating that
our schemes retain the same theoretical guarantees as in the equation setting.
Finally, numerical experiments validate our algorithms and demonstrate their
promising performance compared to state-of-the-art methods.
