$P(x)$ is a polynomial of degree at most $6$ such that $P(1)$, $P(2)$, $P(3)$, $P(4)$, $P(5)$, $P(6)$, and $P(7)$ are $1$, $2$, $3$, $4$, $5$, $6$, and $7$ in some order. What is the maximum possible value of $P(8)$?

Let's think step by step and output the final answer within \boxed{}.
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