After introducing definitions related to the Collatz problem (Part 1), the concept of "verified integers" and several organizational rules around this concept are presented (Part 2). A unique logical tool, the axis of verified integers, is highlighted (Part 3). In Part 4 , it is proven that all bounded trajectories without non-trivial cycles are verified. These elements allow the development of a systematic approach to solving the Collatz problem with the help of inverse graphs (Part 5). The issue of non-trivial cycles and divergent trajectories is then explored (Parts 6 and 7). Ultimately, we arrive at two contradictory propositions :1) Either all integers satisfy the Collatz conjecture, or2) An infinite number of integers do not satisfy it. This eliminates the possibility that only a small number of integers fail to satisfy the conjecture, while the rest do. The conclusion of this study leans toward the first solution : all integers satisfy the Collatz conjecture.This text, written in English, is a translation of the original French text published five months ago on Vixra (Vixra 2410.0063) under the title "New tools to verify the Collatz conjecture". During the translation process, Parts 5, 6 and 7 were extensively revised, resulting in a new text that differs from the initial French version.