We present ci,(2--1) and multi-transition $^{12}$CO observations of a dusty star-forming galaxy, ACT,J2029+0120, which we spectroscopically confirm to lie at $z$,=,2.64. We detect CO(3--2), CO(5--4), CO(7--6), CO(8--7), and ci,(2--1) at high significance, tentatively detect HCO$^{+}$(4--3), and place strong upper limits on the integrated strength of dense gas tracers (HCN(4--3) and CS(7--6)). Multi-transition CO observations and dense gas tracers can provide valuable constraints on the molecular gas content and excitation conditions in high-redshift galaxies. We therefore use this unique data set to construct a CO spectral line energy distribution (SLED) of the source, which is most consistent with that of a ULIRG/Seyfert or QSO host object in the taxonomy of the textit{Herschel} Comprehensive ULIRG Emission Survey. We employ RADEX models to fit the peak of the CO SLED, inferring a temperature of T$sim$117 K and $n_{text{H}_2}sim10^5$ cm$^{-3}$, most consistent with a ULIRG/QSO object and the presence of high density tracers. We also find that the velocity width of the ci line is potentially larger than seen in all CO transitions for this object, and that the $L_{rm C,I(2-1)}/L_{rm CO(3-2)}$ ratio is also larger than seen in other lensed and unlensed submillimeter galaxies and QSO hosts; if confirmed, this anomaly could be an effect of differential lensing of a shocked molecular outflow.
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