During the planning phase of an assurance engagement, one of the key supervisory activities is approving the audit work programs. This step ensures that the planned procedures are appropriate for achieving the engagement objectives and that the audit scope is adequately covered. Supervisory activities like ensuring alignment with engagement objectives, reviewing draft reports, and ensuring workpapers support findings typically occur during the fieldwork or reporting phases. Approving the audit work programs at the planning stage helps to ensure that the engagement is well-directed and thorough.
The Institute of Internal Auditors (IIA) - Standards for the Professional Practice of Internal Auditing, Standard
2200 - Engagement Planning

The most critical situation for the chief audit executive (CAE) to report to the board is the disagreement with the business unit manager's initial decision to accept a particular risk, which was only addressed after discussion with senior management. This situation is critical because it involves a risk that was initially accepted without proper mitigation, which could have significant implications for the organization. Reporting this to the board ensures that they are aware of potential disagreements regarding risk acceptance and management's approach to risk mitigation.
IIA Standards: 2060 - Reporting to Senior Management and the Board
IIA Practice Guide: Reporting to the Board and Senior Management

Application software tracing and mapping tracks the program logic line by line to detect unauthorized code, errors, or inconsistencies. Utility software (A) supports system operations, generalized audit software (B) is used for testing data, and audit expert systems (D) assist with decision-making. For identifying unauthorized code, the best tool is Option C.

Probability-proportional-to-size (PPS) sampling is a technique used to reach conclusions regarding monetary amounts in a population. It is designed to handle variable sampling by focusing on monetary units, making it appropriate for testing account balances. On the other hand, attribute sampling is used to assess the rate of occurrence of a specific characteristic or attribute in a population, such as compliance with a control procedure, and does not focus on monetary amounts.
The Institute of Internal Auditors (IIA) Practice Guide on "Audit Sampling" Generally Accepted Auditing Standards (GAAS)

Comprehensive and Detailed Explanation:
To validate whether risks identified internally reflect industry risks, the auditor should compare the organization's risk profile with peer organizations, industry standards, and external best practices. This process is known as benchmarking (A). Benchmarking helps the auditor assess if management has overlooked emerging or common industry risks.
* Trend analysis (B) evaluates changes over time within the same organization, not external comparison.
* Ratio analysis (C) focuses on financial metrics, not risk identification.
* Observation (D) provides operational insights but not industry comparisons.
Therefore, benchmarking is the correct tool, aligning with IIA guidance that encourages auditors to consider both internal and external environments in risk assessments.