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A line of sight toward the Galactic Center (GC) offers the largest number of potentially habitable systems of any direction in the sky. The Breakthrough Listen program is undertaking the most sensitive and deepest targeted SETI surveys toward the GC. Here, we outline our observing strategies with Robert C. Byrd Green Bank Telescope (GBT) and Parkes telescope to conduct 600 hr of deep observations across 0.7–93 GHz. We report preliminary results from our survey for extraterrestrial intelligence (ETI) beacons across 1–8 GHz with 7.0 and 11.2 hr of observations with Parkes and GBT, respectively. With our narrowband drifting signal search, we were able to place meaningful constraints on ETI transmitters across 1–4 GHz and 3.9–8 GHz with EIRP limits of ≥4 × 10^18 W among 60 million stars and ≥5 × 10^17 W among half a million stars, respectively. For the first time, we were able to constrain the existence of artificially dispersed transient signals across 3.9–8 GHz with EIRP ≥1 × 10^14 W/Hz with a repetition period ≤4.3 hr. We also searched our 11.2 hr of deep observations of the GC and its surrounding region for Fast Radio Burst–like magnetars with the DM up to 5000 pc cm^−3 with maximum pulse widths up to 90 ms at 6 GHz. We detected several hundred transient bursts from SGR J1745−2900, but did not detect any new transient bursts with the peak luminosity limit across our observed band of ≥10^31 erg s^−1 and burst rate of ≥0.23 burst hr^−1. These limits are comparable to bright transient emission seen from other Galactic radio-loud magnetars, constraining their presence at the GC.