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The outflows of oxygen-rich asymptotic giant branch (AGB) stars are thoughtto be driven by radiation pressure by photon scattering on grains with sizes oftenths of microns. The details of the formation of dust in the extendedatmospheres of these stars and the mass-loss process is still not wellunderstood. We obtained quasi-simultaneous observations of the AGB star Mirausing ALMA and ZIMPOL to probe the distribution of gas and large dust grains,respectively. The polarized light images show dust around Mira~A, the companion(Mira~B) and in a trail that connects the two sources. ALMA reveals that dustaround Mira~A is contained in a high-gas-density region with a significantfraction of the polarized light arising from its edge. We constrained the gasdensity, temperature, and velocity within a few stellar radii from the star bymodelling the CO $v=1, J=3-2$ line. We find a mass $(\sim 3.8 \pm 1.3) \times10^{-4}~M_\odot$ to be contained between the stellar millimetre photosphere,$R^{\rm 338~GHz}_\star$, and $4~R^{\rm 338~GHz}_\star$. Our best-fit modelswith lower masses also reproduce the $^{13}$CO $v=0, J=3-2$ line emission fromthis region. We find TiO$_2$ and AlO abundances corresponding to 4.5% and $<0.1$% of the total titanium and aluminium expected for a solar-composition gas.The low abundance of AlO allows for efficient Al depletion into dust alreadyvery close to the star, as expected from thermal dust emission observations andtheoretical calculations of Mira variables. We constrain the presence ofaluminium oxide grains based on the scattered light observations and ourgas-phase model. We find that aluminium oxide grains can account for asignificant fraction of the total aluminium atoms in this region only if thegrains have sizes $\lesssim 0.02~\mu$m. This is an order of magnitude smallerthan the maximum sizes predicted by dust-formation and wind-driving models.

High-resolution observations of gas and dust around Mira using ALMA and SPHERE/ZIMPOL