Symbiotic stars often contain white dwarfs with quasi-steady shell burning on their surfaces. However, in most symbiotics, the origin of this burning is unclear. In symbiotic slow novae, however, it is linked to a past thermonuclear runaway. In June 2015, the symbiotic slow nova AG Peg was seen in only its second optical outburst since 1850. This recent outburst was of much shorter duration and lower amplitude than the earlier eruption, and it contained multiple peaks -- like outbursts in classical symbiotic stars such as Z And. We report Swift X-ray and UV observations of AG Peg made between June 2015 and January 2016. The X-ray flux was markedly variable on a time scale of days, particularly during four days near optical maximum, when the X-rays became bright and soft. This strong X-ray variability continued for another month, after which the X-rays hardened as the optical flux declined. The UV flux was high throughout the outburst, consistent with quasi-steady shell burning on the white dwarf. Given that accretion disks around white dwarfs with shell burning do not generally produce detectable X-rays (due to Compton-cooling of the boundary layer), the X-rays probably originated via shocks in the ejecta. As the X-ray photo-electric absorption did not vary significantly, the X-ray variability may directly link to the properties of the shocked material. AG Pegs transition from a slow symbiotic nova (which drove the 1850 outburst) to a classical symbiotic star suggests that shell burning in at least some symbiotic stars is residual burning from prior novae.
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