Internal audit fraud prevention and detection activities are the best example of an ongoing independent monitoring activity among the options provided. These activities are designed to be independent of the management and are critical in continuously monitoring and identifying potential fraudulent activities within the organization.
IIA standards on fraud and monitoring

The internal audit activity can promote continuous improvement of organizational controls by facilitating control self-assessment (CSA) sessions. These sessions involve managers and staff in evaluating the effectiveness of controls within their areas of responsibility. This approach not only promotes ownership of controls among process owners but also helps identify areas for improvement and fosters a culture of continuous improvement. By engaging managers in these assessments, internal auditors can help ensure that controls are understood, effective, and continually refined based on feedback and changes in the risk environment.
IIA Practice Guide: Control Self-Assessment
IIA Standard 2130: Control

The most important factor in the internal audit activity's independence specified in an internal audit charter is the description of the internal audit activity's reporting structure. This element defines to whom the chief audit executive reports functionally and administratively, which is critical to ensuring the independence and objectivity of the internal audit function from management and other potential sources of bias.
The IIA's International Standards for the Professional Practice of Internal Auditing on independence and objectivity.

The fundamental principle of The IIA ' s Code of Ethics best described as performing work honestly, diligently, and responsibly is Integrity. This principle is foundational to the ethical conduct expected of internal auditors, underpinning their professional behavior and ensuring trust in their work and judgments.
References: The IIA ' s Code of Ethics, specifically the section on Integrity, which outlines the expectation for internal auditors to work with honesty and diligence.

In the scenario where the board requests the chief audit executive (CAE) to provide consulting services for a new systems implementation project, the CAE should avoid making decisions on risk responses within risk management processes. The CAE's role is to provide independent and objective assurance and consulting services. Making decisions on risk responses would impair the CAE's independence and objectivity, which are crucial for the internal audit function. Instead, the CAE can provide advice and recommendations on risk management practices while ensuring that management retains responsibility for decision-making.
The IIA Standards: Standard 1112 - Chief Audit Executive Roles Beyond Internal Auditing: "If the CAE has or is expected to have roles and/or responsibilities that fall outside of internal auditing, safeguards must be in place to limit impairments to independence or objectivity." The IIA Practice Guide: "Independence and Objectivity": Discusses the importance of maintaining independence and objectivity in consulting engagements.