A way to reach exactness from current probabilistic models is to ask them to build a deterministic system. Then you won't directly employ the LLM services, but

A way to reach exactness from current probabilistic models is to ask them to build a deterministic system. Then you won't directly employ the LLM services, but instead use the output of the system the LLM built. This system may be flawed, but it's easier to get it to behave deterministically and amenable to analysis and correction.