  Abridged: Direct imaging has made significant progress over the past decade
leading to the detection of several giant planets. Observing strategies and
data rates vary from instrument to instrument and wavelength, and can result in
tens of thousands of images to be combined. We here present a new approach,
tailored for VLT/NaCo observations performed with the Annular Groove Phase Mask
(AGPM) coronagraph at $L'$ filter. Our pipeline aims at improving the
post-processing of the observations on two fronts: identifying the location of
the star behind the AGPM to better align the science frames and performing
frame selection. Our method relies on finding the position of the AGPM in the
sky frame observations, and correlate it with the circular aperture of the
coronagraphic mask. This relationship allows us to retrieve the location of the
AGPM in the science frames, in turn allowing us to estimate the position of the
star. In the process we also gather additional information useful for our frame
selection approach. We tested our pipeline on several targets, and find that we
improve the S/N of companions around $\beta$ Pictoris and R CrA by $24\pm3$ \%
and $117\pm11$ \% respectively, compared to other state-of-the-art reductions.
The astrometry of the point sources is slightly different but remains
compatible within $3\sigma$ compared to published values. Finally, we find that
even for NaCo observations with tens of thousands of frames, frame selection
yields just marginal improvement for point sources but may improve the final
images for objects with extended emission such as disks. We proposed a novel
approach to identify the location of the star behind a coronagraph even when it
cannot easily be determined by other methods, leading to better S/N for nearby
point sources, and led a thorough study on the importance of frame selection,
concluding that the improvements are marginal in most case.
