  We introduce a new Monte Carlo template-based reconstruction method for air
shower arrays, with a focus on shower core and energy reconstruction of
$\gamma$-ray induced air showers. The algorithm fits an observed lateral
amplitude distribution of an extensive air shower against an expected
probability distribution using a likelihood approach. A full Monte Carlo air
shower simulation in combination with the detector simulation is used to
generate the expected probability distributions. The goodness of fit can be
used to discriminate between $\gamma$-ray and hadron induced air showers. As an
example, we apply this method to the High Altitude Water Cherenkov $\gamma$-ray
Observatory and its recently installed high-energy upgrade. The performance of
this method and the applicability to air shower arrays with mixed detector
types makes it a promising reconstruction approach for current and future
instruments.
