  We prove that it is consistent that Club Stationary Reflection and the
Special Aronszajn Tree Property simultaneously hold on $\omega_2$, thereby
contributing to the study of the tension between compactness and incompactness
in set theory. The poset which produces the final model follows the collapse of
an ineffable cardinal first with an iteration of club adding (with
anticipation) and second with an iteration specializing Aronszajn trees. In the
first part of the paper, we prove a general theorem about specializing
Aronszajn trees on $\omega_2$ after forcing with what we call
$\mathcal{F}$-Strongly Proper posets, where $\mathcal{F}$ is either the weakly
compact filter or the filter dual to the ineffability ideal. This type of
poset, of which the Levy collapse is a degenerate example, uses systems of
exact residue functions to create many strongly generic conditions. We prove a
new result about stationary set preservation by quotients of this kind of
poset; as a corollary, we show that the original Laver-Shelah model, which
starts from a weakly compact cardinal, satisfies a strong stationary reflection
principle, though it fails to satisfy the full Club Stationary Reflection. In
the second part, we show that the composition of collapsing and club adding
(with anticipation) is an $\mathcal{F}$-Strongly Proper poset. After proving a
new result about Aronszajn tree preservation, we show how to obtain the final
model.
