  Associated to a family of $G$-$\ast$-endomorphisms on a $G$-C*-algebra $A$
satisfying certain minimality conditions, we give a $G$-C*-correspondence
$\mathcal{E}$ over $A$ whose Cuntz--Pimsner algebra $\mathcal{O}_\mathcal{E}$
is simple. For certain quasi-free flows $\gamma$ (commuting with the
$G$-action) on $\mathcal{O}_\mathcal{E}$, we further prove the simplicity of
the reduced crossed product $\mathcal{O}_\mathcal{E} \rtimes_\gamma
\mathbb{R}$. We then classify the KMS weights of $\gamma$. This in particular
gives a sufficient condition for $\mathcal{O}_\mathcal{E}$ and
$\mathcal{O}_\mathcal{E}\rtimes_\gamma \mathbb{R}$ to be stably finite (and to
be stably projectionless). As the amenability of $G \curvearrowright A$
inherits to the induced actions $G \curvearrowright \mathcal{O}_\mathcal{E},
\mathcal{O}_\mathcal{E}\rtimes_\gamma \mathbb{R}$, this provides a new
systematic framework to provide amenable actions on stably finite simple
C*-algebras.
