One take  toward reasoning .... using current LLM.

some excerpt:

"

Algorithm-of-Thoughts (AoT)

Maintains a single evolving context chain, eliminating the need for redundant queries as in the Tree-of-Thought. It explores a mutable path of reasoning.

While ToT and GoT address the LLM reasoning challenge through search-based mechanisms, producing a myriad of reasoning paths in graph forms. However, their heavy reliance on numerous LLM queries, sometimes numbering in the hundreds for a singular problem, poses computational inefficiencies.

The Algorithm-of-Thoughts (AoT) offers an innovative method that features a dynamic and mutable reasoning path. By maintaining a single evolving thought context chain, AoT consolidates thought exploration, enhancing efficiency and reducing computational overhead.

"

Source: 

https://towardsdatascience.com/something-of-thought-in-llm-prompting-an-overview-of-structured-llm-reasoning-70302752b390

SCI's approach toward same objective is different ..I might publish it sometime later.