There are several synonyms that can be used in place of the phrase "mutually testing." One option is "reciprocal assessment," which implies that both parties are evaluating each other in an equal manner. Another possibility is "joint examination," indicating that there is a collaborative effort to assess each other's abilities or performance. "Bilateral evaluation" is another synonym that could be used, emphasizing the idea of two parties evaluating each other. Alternatively, "shared scrutiny" or "mutual inspection" could be used, both of which suggest a thorough examination or analysis. Overall, there are many synonyms to choose from when trying to communicate the idea of two parties testing or assessing each other.