  We demonstrate that triangle singularity (TS) and box singularity (BS)
mechanisms can produce unique narrow enhancements at the $\Lambda_c\bar{D}$ and
$\Lambda_c\bar{D}^*$ thresholds in the invariant mass spectra of $J/\psi p$ and
$J/\psi p\pi$, respectively. Taking into account that such mechanisms only
depend on the initial $\Sigma_c^{(*)}\bar{D}^{(*)}$ interactions near threshold
within the TS or BS kinematic regimes, the $\Lambda_c\bar{D}$ and
$\Lambda_c\bar{D}^*$ threshold enhancements can be regarded as a feed-down
phenomenon originated from both the heavier pentaquark decays and the
$\Sigma_c^{(*)}\bar{D}^{(*)}$ scatterings from the continuum. A search for
these structures in the $J/\psi p$ and $J/\psi p\pi$ spectra in both exclusive
and semi-inclusive processes will provide a smoking-gun evidence for the
hadronic molecule nature of those observed pentaquarks and clarify the role
played by the TS and BS in the near-threshold dynamics.
