A partnership opportunity has arisen at the local office of Sam, Alan, and Patrick $($SAP$),$ a regional CPA firm, due to increased revenues. This has sparked competition among managers aspiring for partnership. Helena Liu, a senior audit manager and the current favorite for the role, has a track record of favorable performance evaluations and technical competence. However, her final hurdle to partnership is to demonstrate her ability to conduct audit engagements with the genuine, accurate, and complete objectives. Helena's client is Comfort Inn Limited $($CIL$),$ a small hotel providing accommodation, catering, and conference facilities. Employing $100$ people, CIL operates with a traditional manual accounting system. Helena has completed six tasks and is required to provide an explanation for each of her actions. The tasks are as follows:

$(1)$ She conducts test counts by choosing items from the inventory list and physically locating them in the warehouse.

$(2)$ She acquires the aged trial balance of receivables and verify the total balance against the general ledger.

$(3)$ She selects invoices and credit notes from periods before and after year$-$end to ensure proper recording.

$(4)$ She verifies the cost of non$-$current assets by cross$-$referencing purchase invoices and checking depreciation rates and calculations.

$(5)$ She rechecks calculations on invoices, payroll, etc., and review control account reconciliations.

$(6)$ She examines property deeds to confirm the company's legal ownership of the reported properties.

Please identify the most likely general heading of audit objectives $($i$.$e$.,$ genuine, complete, accurate$)$ applicable to the above tasks $1-6$ and provide a brief explanation of why Helena is performing each task.