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The Free-Electron Laser (FEL) FLASH offers the worldwide still unique capability to study ultrafast processes with high-flux, high-repetition rate XUV and soft X-ray pulses. The vast majority of experiments at FLASH are of pump-probe type. Many of them rely on optical ultrafast lasers. Here, a novel FEL facility laser is reported which combines high average power output from Yb:YAG amplifiers with spectral broadening in a Herriott-type multi-pass cell and subsequent pulse compression to sub-100 fs durations. Compared to other facility lasers employing optical parametric amplification, the new system comes with significantly improved noise figures, compactness, simplicity and power efficiency. Like FLASH, the optical laser operates with 10 Hz burst repetition rate. The bursts consist of 800 $\mu$s long trains of up to 800 ultrashort pulses being synchronized to the FEL with femtosecond precision. In the experimental chamber, pulses with up to 50 $\mu$J energy, 60 fs FWHM duration and 1 MHz rate at 1.03 $\mu$m wavelength are available and can be adjusted by computer-control. Moreover, nonlinear polarization rotation is implemented to improve laser pulse contrast. First cross-correlation measurements with the FEL at the plane-grating monochromator photon beamline are demonstrated, exhibiting the suitability of the laser for user experiments at FLASH., Comment: 28 pages, 13 figures