Four numbers, \( a, b, c, \) and \( d \), are such that \( a + b = 15 \), \( b + c = 20 \), \( c + d = 25 \), and \( d + a = 30 \). Use logical deduction and elimination methods to find the values of \( a, b, c, \) and \( d \). What is the value of \( a \)? Let's think step by step and output the final answer within \boxed{}.
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