A triangle has side lengths of \( a \), \( b \), and \( c \), where \( a \), \( b \), and \( c \) are positive integers. Given that \( a = 9 \), \( b = 14 \), and \( c \) is an unknown positive integer, what is the range of possible integer values for \( c \) such that the triangle inequality theorem holds? What is the least possible perimeter of this triangle? Let's think step by step and output the final answer within \boxed{}.
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