Regular Languages - Infiniteness Problem

A Deterministic Finite Automaton is given to you in the form of a black box, i.e, you are only allowed to enter strings and check if it accepts but not allowed to examine the internal workings of the automaton.

If you're given that the automaton has 23 states, what is the length of the largest string you need to test before you can be sure that the Regular Language accepted by the automaton is finite?

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