Please answer the following question:

Acme Corp, a publicly traded company, is in the widget industry. In recent years, Acme has faced declining profitability and decreasing stock value. Jane Smith, Acme's CEO and a significant shareholder, recently received a buyout offer from Omega Inc., a key competitor. Jane and the Acme Board of Directors (BoD) engaged in limited negotiations with Omega Inc. Jane did not disclose to the BoD that she was promised a lucrative position in Omega Inc. after the acquisition. Believing the price offered was the best Acme could get, the BoD agreed to a "no-shop" clause prohibiting Acme from seeking or entertaining other offers. Subsequently, Beta Co., another key player in the industry, approached an Acme board member expressing a willingness to buy Acme at a 20% premium to the Omega offer. Given the no-shop clause, the BoD did not pursue the offer, nor did it notify the shareholders about Beta Co.'s interest. Acme's shareholders are upset about the declined offer from Beta Co., especially given that it was significantly higher than Omega's offer. A group of minority shareholders has now filed suit against Acme's BoD and Jane Smith, claiming breaches of fiduciary duties. Question What fiduciary duties did Jane Smith owe to Acme's shareholders, and did she breach any of those duties based on the facts provided? Explain