  Low mass-ratio (q) contact binary systems are progenitors of stellar mergers
such as blue straggles (BS) or fast-rotating FK Com stars. In this study, we
present the first light curve analysis of two newly identified low mass-ratio
contact binary systems, TIC 55007847 and TIC 63597006, that are identified from
TESS. Both stars are classified as A-subtype contact binaries. We obtained the
precise orbit periods for the two objects by using the O-C method, i.e.
P=0.6117108 d for TIC 55007847 and P=0.7008995 d for TIC 63597006,
respectively, and found an obvious periodic signal in the O-C curve of TIC
63597006. We suggest that the periodic signal comes from a third body. We
further use the Markov Chain Monte Carlo (MCMC) method with PHOEBE to derive
the photometric solutions for the two binaries. The photometric solution for
this object shows that the contribution of the third body is about 6%. Our
analysis revealed that TIC 55007847 has an extremely low mass ratio of q=0.08.
By calculating the ratio of spin angular momentum to the orbital angular
momentum Js/Jo, we found that TIC 55007847 is very close to the instability
threshold with Js/Jo = 0.31, indicating that it may merge into a single,
fast-rotating star in the future. For TIC 63597006, q=0.14 and Js/Jo=0.15. This
object is in a relatively stable evolutionary status at present.
