One way would be this:

next if $field =~ /^(first|second|third)$/;
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The '^' matches the beginning of a string, and the '$' matches the end, emulating an 'eq' function for whatever's in between them. The '|'s are roughly equivalent to an 'or' statement: this will match 'first' or 'second' or 'third'.

Update: added explanation, and parens, thanks to Enlil.
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Love justice; desire mercy.