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If the tank is slow to fill then you need to replace the fill valve (see attached pic). A Fluidmaster fill valve is what you need. They are inexpensive and widely available. Once yo replace the fill valve that may solve the problem but you can also try cleaning out the siphon jet (the ~3/4" hole in the bottom of the bowl below the water line). If this hole gets clogged up it can hinder the flushing action.
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