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As the pertaining energy scale is yet unknown, new colliders are in order to try to pin down their origin. The choice of the right machine(s) to achieve this goal can be enlightened by the successes of past History. Between the late 70's to the early 90's, precision measurements of neutral currents first led to the prediction of the W and Z masses; the W and Z were then discovered at the CERN S${\rm p\bar p}$S at the predicted masses, and the CERN LEP measured the gauge sector properties with precision. Similarly, in the 90's, the precise measurements of the gauge sector led to the prediction of the top quark mass, later discovered at the FNAL Tevatron at the predicted mass, and in the last decade, the precise measurements of the W mass at the FNAL Tevatron led to the prediction of the Higgs boson mass, later discovered at the CERN LHC at the predicted mass.   To continue this success story, the next facility should be a able to nail down all the Electroweak Symmetry Breaking parameters,with precision measurements of the Z, W, top and Higgs properties,  towards a prediction of the new physics energy scale. The next-to-next facility would then aim at discovering this new physics directly with access to much larger centre-of-mass energies. The recent update of the European Strategy, approved at the end of May by the CERN Council, does not say anything different. To proceed with the choice, the following questions must be answered: \begin{itemize}  \item What is the potential of (HL-) LHC to meet these objectives ?   \item What parameters must be measured and with what precisions ?  \item What energy scale should be aimed at to directly look for new physics ?  \item What are the accelerators to optimally achieve these goals goals, and what is the potential of (HL-) LHC  ? \item When is the decision to be taken ?  \end{itemize}  Mention the European Strategy. State the precision needed for EWSB parameters and Higgs boson couplings. with precision measurements of the Z, W, top and Higgs properties,  List the proposal for Higgs factories able to perform all these measurements.