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Cosmic strings are the linear topological defects which could have formed in the early Universe in phase transitions of the vacuum. The existence of cosmic strings does not contradict to modern observational data (space missions WMAP and Planck), although cosmic strings are still not discovered. Despite the complexity of the cosmological scenario about the cosmic strings, that still stands in the way of a complete understanding; a promising strategy is described here, aimed at detecting these elusive physical entities. Our procedure is a mix of the two main methods of the cosmic string search. The first one is the analysis of anisotropy of the CMB radiation. So, moving cosmic string due to the Doppler effect creates a specific form of the anisotropy on the surface of last scattering. Having a step-like structure, this anisotropy can be found by convolution of the radio maps (WMAP and Planck) with a set of orthogonal step functions. This method has allowed to identify several cosmic strings candidates, the most reliable of which (Cosmic String candidate No. 1 = CSc-1) has an amplitude of anisotropy at 40 µK. The second method is the search of the strong gravitational lensing effects of remote sources by a string. A remote source (a galaxy) behind the cosmic string at a certain angular distance from it, generates two gravitational-lens images, characterized by identical spectra, identical redshifts and the special morphological features. In a previous work the convolution of WMAP and Planck CMB radio maps by the modified Haar functions provided a list of preliminary CS candidates with the amplitude 40 µK. For the best one (CSc-1), we carried on an independent optical analysis, based on the search of sources of strong gravitational lensing. Using a photometric criterion we identified (by preliminary visual inspection) 42 lens candidates. This number seems convincingly in excess over the density of strong gravitational lenses in ordinary fields (a good hint for presence of a cosmic string). From the final catalog of the all close pairs of object in each optical field we estimated the mean deficit angle [3.5'',6.5]; so the CSc-1 velocity is [0.4c, 0.7c]. The accurate confirmation of the gravitational nature of the lens candidates must be done by their spectra. We plan to do it as well as to continue the study of the spectral and morphological features of the lens candidates along the CSc-1. The discovery of cosmic strings would serve as the first observational investigation of the fundamental theory of superstring, and would also weed out a number of theoretical models of the early Universe.