  Are WO-type Wolf Rayet (WR) stars in the final stage of massive star
evolution before core-collapse? Although WC- and WO-type WRs have very similar
spectra, WOs show a much stronger O VI $\lambda \lambda$3811,34 emission-line
feature. This has usually been interpreted to mean that WOs are more oxygen
rich than WCs, and thus further evolved. However, previous studies have failed
to model this line, leaving the relative abundances uncertain, and the
relationship between the two types unresolved. To answer this fundamental
question, we modeled six WCs and two WOs in the LMC using UV, optical, and NIR
spectra with the radiative transfer code CMFGEN in order to determine their
physical properties. We find that WOs are not richer in oxygen; rather, the O
VI feature is insensitive to the abundance. However, the WOs have a
significantly higher carbon and lower helium content than the WCs, and hence
are further evolved. A comparison of our results with single-star Geneva and
binary BPASS evolutionary models show that while many properties match, there
is more carbon and less oxygen in the WOs than either set of evolutionary model
predicts. This discrepancy may be due to the large uncertainty in the
$^{12}$C+$^4$He$\rightarrow^{16}$O nuclear reaction rate; we show that if the
Kunz et al. rate is decreased by a factor of 25-50%, then there would be a good
match with the observations. It would also help explain the LIGO/VIRGO
detection of black holes whose masses are in the theoretical upper mass gap.
