7. Given a cube $A B C D-A_{1} B_{1} C_{1} D_{1}$ with edge length 1, point $P$ is on edge $B C$, and point $Q$ is the midpoint of edge $C C_{1}$. If the plane passing through points $A, P, Q$ intersects the cube to form a pentagon, then the range of $B P$ is $\qquad$ .
Answer: 
As shown in the figure, when $B P \in\left(\frac{1}{2}, 1\right)$, the cross-section is a pentagon.