💡 Detailed Explanation
The correct answer is '斡旋' (assen). '斡旋' refers to acting as an intermediary to help two parties come to an agreement or establish a relationship, especially in a formal context like job placement or business deals. It is the most appropriate term for a public institution formally arranging employment. '仲介' (chūkai) is similar but more general (e.g., real estate brokerage). '紹介' (shōkai) is simply an 'introduction'. '調停' (chōtei) is specifically for 'mediation' in a dispute or conflict.