  We present a detailed analysis of two fields located 26 kpc (~5 scalelengths)
from the centre of M31. One field samples the major axis populations--the Outer
Disc field--while the other is offset by ~18' and samples the Warp in the
stellar disc. The CMDs based on HST/ACS imaging reach old main-sequence
turn-offs (~12.5 Gyr). We apply the CMD-fitting technique to the Warp field to
reconstruct the star formation history (SFH). We find that after undergoing
roughly constant SF until about 4.5 Gyr ago, there was a rapid decline in
activity and then a ~1.5 Gyr lull, followed by a strong burst lasting 1.5 Gyr
and responsible for 25% of the total stellar mass in this field. This burst
appears to be accompanied by a decline in metallicity which could be a
signature of the inflow of metal-poor gas. The onset of the burst (~3 Gyr ago)
corresponds to the last close passage of M31 and M33 as predicted by detailed
N-body modelling, and may have been triggered by this event. We reprocess the
deep M33 outer disc field data of Barker et al. (2011) in order to compare
consistently-derived SFHs. This reveals a similar duration burst that is
exactly coeval with that seen in the M31 Warp field, lending further support to
the interaction hypothesis. The complex SFHs and the smoothly-varying
age-metallicity relations suggest that the stellar populations observed in the
far outer discs of both galaxies have largely formed in situ rather than
migrated from smaller galactocentric radii. The strong differential reddening
affecting the CMD of the Outer Disc field prevents derivation of the SFH.
Instead, we quantify this reddening and find that the fine-scale distribution
of dust precisely follows that of the HI gas. This indicates that the outer HI
disc of M31 contains a substantial amount of dust and therefore suggests
significant metal enrichment in these parts, consistent with inferences from
our CMD analysis.
