Expected value of the $k$'th order statistic given that it's smaller than $\tau$

Question

Let $X_1,\ldots,X_n\sim U[0,1]$ be i.i.d. uniform random variables and let $X_{(k)} $ denote the $k$'th smallest variable.

Given some $\tau\in(0,1)$, what is $$\mathbb E[X_{(k)}\mid X_{(k)}\le \tau]?$$

Can we give a simple-to-use lower bound if the exact expression is not simple?