Let $a$, $b$, $c$ be positive integers and $p$ be a prime number. Assume that 
\[ a^n(b+c)+b^n(a+c)+c^n(a+b) \equiv 8 \pmod{p} \] 
for each nonnegative integer $n$. Let $m$ be the remainder when $a^p+b^p+c^p$ is divided by $p$, and $k$ the remainder when $m^p$ is divided by $p^4$. Find the maximum possible value of $k$.

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