In this paper we propose a method for the adaptive complex assessment (ACA) of the higher-order thinking (HOT) skills needed by students for problem solving, and we examine the impact of the method on the development of HOT skills in a problem-based learning (PBL) environment. Complexity in the assessment is provided by initial, formative, and adaptive assessments of HOT skills; assessments of collaborative skills; and summative assessments of HOT skills. Adaptability in the assessment is provided through the dynamics of an instructor's assessments based on developing HOT skills; through a flexible choice of control tests and instructional problems for students and collaborative groups; and through the self-formation of heterogeneous, collaborative HOT skill groups. The assessment fosters the development of HOT and collaborative skills through a combination of personalized and collaborative problem-based learning (PBL). The three-stage assessment process guides the development of HOT skills during subject study through PBL. The focus of the first stage is on developing the HOT skills of students through personalized PBL. The second stage is devoted to developing HOT skills and collaborative skills through collaborative PBL. The third stage is devoted to assessing collaborative skills and constructing summative assessments of students. The proposed calculations for the coefficients of HOT skill development serve as a constructive means of exploring the impact of the ACA method on the HOT skill development of students.