Let \( n \) be the integer such that \( 0 \le n < 41 \) and \( 5n \equiv 2 \pmod{41} \). What is \( (3^n)^2 + 5 \pmod{41} \)?
Express your answer as an integer from \( 0 \) to \( 40 \), inclusive. Let's think step by step and output the final answer within \boxed{}.
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