  We prove that the ACC conjecture for minimal log discrepancies holds for
threefolds in $[1-\delta,+\infty)$, where $\delta>0$ only depends on the
coefficient set. We also study Reid's general elephant for pairs, and show
Shokurov's conjecture on the existence of $(\epsilon,n)$-complements for
threefolds for any $\epsilon\geq 1$. As a key important step, we prove the
uniform boundedness of divisors computing minimal log discrepancies for
terminal threefolds. We show the ACC for threefold canonical thresholds, and
that the set of accumulation points of threefold canonical thresholds is equal
to $\{0\}\cup\{\frac{1}{n}\}_{n\in\mathbb Z_{\ge 2}}$ as well.
