ReLU With the Corner Sanded Off

ReLU has a sharp corner at $0$, where its slope jumps straight from $0$ to $1$ with nothing in between. Softplus is a smooth stand-in that looks like ReLU from a distance but rounds the corner off:

Far to the left it hugs $0$. Far to the right it hugs the line $y = x$. Near $0$ it bends smoothly, so its slope changes gradually instead of jumping.

Task: write softplus_with_slope(values). For each pre-activation $x$ in the list values, produce the pair [softplus(x), slope], where slope is the derivative of softplus at $x$. Round both numbers to 4 decimal places and return the pairs as a list, in the same order as the input. An empty list gives an empty list.

The layer this runs in sees pre-activations as large as $\pm 1000$. Your function must return correct, finite numbers for them, and must not crash.