The Municipal Public Library has $516$ employees, including $163$ librarians. A recent study reveals a stark gender imbalance among branch supervisors: $70\%$ are male, while only $30\%$ are female, despite men comprising only $25\%$ of all branch librarians. In response, the library implements an affirmative action plan that considers an applicant's gender as one factor when filling supervisory positions until the gender imbalance is rectified. The plan does not provide for a quota or a specific attainment goal.

James Moore, a male librarian with $15$ years of experience and consistently excellent performance reviews applies for a vacant supervisory position. He is demonstrably the most qualified candidate, scoring highest on all objective assessments and interviews. However, he is ultimately passed over in favor of Sarah Jones, a female librarian with $10$ years of experience and solid performance. Although she performed well in the assessments and interviews, her performance was slightly below James' level of qualification. However, since the Municipal Library determined that both candidates were qualified for the position, it offered Sarah Jones the position based on the affirmative action plan.

James Moore sued the Municipal Library under Title VII claiming unlawful discrimination.

Is the Library's affirmative action plan valid