The High Altitude Water Cherenkov (HAWC) gamma-ray observatory detects cosmic- and
gamma-ray initiated air showers in the TeV energy range using 300 water Cherenkov detectors
(WCDs). To improve its sensitivity at the highest energies, HAWC has been upgraded with a
sparse array of 345 small WCDs (outrigger array) around the HAWC main array. The outrigger
array increases the instrumented area of HAWC by a factor of 4 and has started taking data since August 2018. A new gamma-ray reconstruction method has been developed to improve the reconstruction of the air showers which combines the data of mixed type particle detector arrays. In this contribution, we will show the first results of the combined air shower reconstruction of HAWC and its outrigger array using Monte Carlo simulations and the first combined experimental data set.