Is This Evaluator-Optimizer, or Does It Need to Be an Agent?

A team builds a system that generates SQL queries from natural- language analytics questions: one call generates a candidate query, a second call checks the query against the database schema for column/table existence and syntax validity, and if it fails the check, the critique is fed back to the generator for another attempt, up to 3 rounds, after which the system gives up and asks the user to rephrase.

1. Name the pattern and justify it precisely against the bounded- vs-open-ended distinction this subject draws.
2. The team later wants to add: "if the query runs successfully but returns zero rows, try reformulating the question's intent and regenerate." Does this addition change which pattern this is? Why or why not?
3. Propose one further addition that would push this system across the Level 1 / Level 2 boundary, and explain exactly what changes.