  The outflowing molecular gas in the circumnuclear disk (CND) of the nearby
(D=14 Mpc) AGN-starburst composite galaxy NGC 1068 is considered as a
manifestation of ongoing AGN feedback. The large spread of velocities from the
outflowing gas is likely driving various kinds of shock chemistry across the
CND. We performed a multiline molecular study using CH3OH with the aim of
characterizing the gas properties probed by CH3OH in the CND of NGC 1068, and
investigating its potential association with molecular shocks. Multi-transition
CH3OH were imaged at the resolution of 0.''5-0.''8 with the Atacama Large
Millimeter/submillimeter Array (ALMA). We performed non-LTE radiative transfer
analysis coupled with a Bayesian inference process in order to determine the
gas properties such as the gas volume density and the gas kinetic temperature.
The gas densities traced by CH3OH point to $\sim 10^{6}$ cm\textsuperscript{-3}
across all the CND regions. The gas kinetic temperature cannot be well
constrained in any of the CND regions though the inferred temperature is likely
low ($\lesssim 100$ K).The low gas temperature traced by CH3OH suggests shocks
and subsequent fast cooling as the origin of the observed gas-phase CH3OH
abundance. We also note that the E-/A- isomer column density ratio inferred is
fairly close to unity, which is interestingly different from the Galactic
measurements in the literature. It remains inconclusive whether CH3OH
exclusively traces slow and non-dissociative shocks, or whether the CH3OH
abundance can actually be boosted in both fast and slow shocks.
