  Based upon our recent study, we reveal the profound physical content of the
longitudinal-Goldstone boson equivalence theorem as being able to discriminate
physical processes which are sensitive/insensitive to probing the electroweak
symmetry breaking (EWSB) sector. We then develop a precise electroweak power
counting rule (a generalization from Weinberg's counting method) to
`separately' count the power dependences on the energy E and all relevant mass
scales. With these, we analyze the complete set of the bosonic operators in the
electroweak chiral Lagrangian and systematically estimate and classify the
sensitivities for testing all these effective operators at the CERN LHC via the
weak-boson fusions and quark-anti-quark annihilations. These two kinds of
processes are shown to be `complementary' in probing the EWSB mechanism.
