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Amplified bursts of laser pulses are sought for various machining, deposition, spectroscopic and strong-field applications. Standard frequency- and time-domain techniques for pulse division become inadequate when intraburst repetition rates reach the terahertz (THz) range as a consequence of inaccessible spectral resolution, requirement for interferometric stability, and collapse of the chirped pulse amplification (CPA) concept due to the loss of usable bandwidth needed for safe temporal stretching. Avoiding the burst amplification challenge and resorting to a lossy post-division of an isolated laser pulse after CPA leaves the limitations of frequency- and time-domain techniques unsolved. In this letter, we demonstrate an approach that successfully combines amplitude and phase shaping of THz bursts, formed using the Vernier effect, with active stabilization of spectral modes and efficient energy extraction from a CPA regenerative amplifier. As proof of concept, the amplified bursts of femtosecond near-infrared pulses are down-converted into tunable THz-frequency pulses via optical rectification.