  The $^{12}$C($\alpha,\gamma$)$^{16}$O reaction, an important component of
stellar helium burning, plays a key role in nuclear astrophysics. It has direct
impact on the evolution and final state of massive stars, while also
influencing the elemental abundances resulting from nucleosynthesis in such
stars. Providing a reliable estimate for the energy dependence of this reaction
at stellar helium burning temperatures has been a major goal for the field. In
this work, we study the role of potential new measurements of the inverse
reaction, $^{16}$O($\gamma,\alpha$)$^{12}$C, in reducing the overall
uncertainty. A multilevel R-matrix analysis is used to make extrapolations of
the astrophysical S factor for this reaction to the stellar energy of 300 keV.
The statistical precision of the S-factor extrapolation is determined by
performing multiple fits to existing E1 and E2 ground state capture data,
including the impact of possible future measurements of the
$^{16}$O($\gamma,\alpha$)$^{12}$C reaction. In particular, we consider a
proposed JLab experiment that will make use of a high-intensity low-energy
bremsstrahlung beam that impinges on an oxygen-rich single-fluid bubble chamber
in order to measure the total cross section for the inverse reaction. The
importance of low energy data as well as high precision data is investigated.
