1 day pass + half-fare card in swiss

How does the day pass work and is it only available for half-fare pass holders? ill be in Zurich on May 19-22 and im planning of taking a day trip from Winterthur to Interlaken or Luzern. actually someone suggested to me with the limited time i have i should visit Luzern instead and do Pilatus loop or the Mt Rigi loop or Mt Titlis. are these places covered with 1 day pass? or what swiss pass should i get for the 3days in switzerland? thank you

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