Consider the following function:

$$f(x) = \begin{cases} 2 x^2 + 3 x + 3 & x \leq 1 \\ a x+4 & x > 1\\ \end{cases}$$

Find a value of $a$ such that the function is differentiable everywhere. If no such value of $a$ exists, enter '$DNE$'.
$a =$