Assume that a directed graph is finite, has one single start node and one single goal node, has positive weights $($costs$)$ for all edges, and has no circular paths. What are the correct statements for the search algorithm in this directed graph? Select all that apply:

UCS search is always complete and optimal.

UCS search might not always be complete or optimal.

A$*$ search is always complete and optimal.

Depending on the heuristic, A$*$ search might not always be complete or optimal.