elementary number theory - Proof that $n! > 3n$ for $nge4 $ using the Principle of Mathematical Induction

Use induction to prove that $n! > 3n$ for $n\ge4 $.

I have done the base case and got both sides being equal to $24>12$ for $n=4$.
However, when doing the inductive step I can't seem to find the right form to match the expression on the right hand side.

So far I have:

Need to show: $(n+1)!>3(n+1)$.

When doing the inductive step:

$(n+1)! = (n+1)n!$

we know that $n!$ is larger than $3n$, then

$(n+1)n! >(n+1)3n$.

Here is where I don't know what to do next, could anyone shed some insight on how to continue after this part? Thanks.