Route through a taxonomy with chained Choices and beam search

Each internal node of the taxonomy becomes a Choice whose options show their own description plus a contains map of the children, so the model can see the leaves before committing to a branch. beam_search keeps the best $K$ paths by the geometric mean of edge probabilities, $\exp(\text{mean}(\log p_i))$ (the numerically safer form the cookbook suggests), and each round asks one Choice per unfinished path in a single request. Greedy search is the same function with $K = 1$. The decision that matters most is building the trap before trusting either: a case where the top-level winner leads nowhere clear, so you can see greedy fail and beam recover.