Consider the following problem, which is an example from a benchmark designed to test the reasoning capabilities of advanced AI models:

A mathematical structure is defined by the set of all integers and an operation *such that for any two integersaandb, a * b = a + b + 1. This structure forms a group. What is the inverse of an element a within this group?

Briefly explain two distinct features of this problem that make it a challenging test of an AI's reasoning abilities, as opposed to a simple test of knowledge retrieval.