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Laser-plasma accelerators (LPAs) produce electric fields of the order of 100 GV m⁻¹, more than 1000 times larger than those produced by radio-frequency accelerators. These uniquely strong fields make LPAs a promising path to generate electron beams beyond the TeV, an important goal in high-energy physics. Yet, large electric fields are of little benefit if they are not maintained over a long distance. It is therefore of the utmost importance to guide the ultra-intense laser pulse that drives the accelerator. Reaching very high energies is equally useless if the properties of the electron beam change completely from shot to shot, due to the intrinsic lack of stability of the injection process. State-of-the-art laser-plasma accelerators can already address guiding and control challenges separately by tweaking the plasma structures. However, the production of beams that are simultaneously high quality and high energy has …