You should:
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1) BOTH begin — and end — the original quote with a traditional quotation mark ; AND:
2) Use a 'single quotation mark' to BOTH begin — and end — the quotation that is inside the original quote.
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Note the traditional quotation marks: “…” ;
or, simply: "...." {for the traditional quotation marks}.
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Note the "single quotation marks" : ‘…’ ;
or, simply: '…' {which resemble apostrophe symbols} for
the single quotation marks.
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