Symbiotic stars are long-orbital-period interacting-binaries characterized by extended emission over the whole electromagnetic range and by complex photometric and spectroscopic variability. In this paper, the first of a series, we present OGLE light curves of all the confirmed symbiotic stars in the Large Magellanic Cloud, with one exception. By careful visual inspection and combined time-series analysis techniques, we investigate for the first time in a systematic way the photometric properties of these astrophysical objects, trying in particular to distinguish the nature of the cool component (e.g., Semi-Regular Variable vs. OGLE Small-Amplitude Red Giant), to provide its first-order pulsational ephemerides, and to link all this information with the physical parameters of the binary system as a whole. Among the most interesting results, there is the discovery of a 20-year-long steady fading of Sanduleaks star, a peculiar symbiotic star known to produce the largest stellar jet ever discovered. We discuss by means of direct examples the crucial need for long-term multi-band observations to get a real understanding of symbiotic and other interacting binary stars. We eventually introduce BOMBOLO, a multi-band simultaneous imager for the SOAR 4m Telescope, whose design and construction we are currently leading.
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