Final answer:
The control activity most likely to assist in satisfying the completeness assertion for long-term investments is the comparison of securities in the bank safe deposit box with recorded investments by an internal auditor.
Step-by-step explanation:
To satisfy the completeness assertion related to long-term investments, an entity would most likely use the control activity where the internal auditor compares the securities in the bank safe deposit box with recorded investments. This procedure ensures that all investments which the entity has made are properly recorded on the balance sheet, and that there are no omissions. It's vital in the audit process to verify that all transactions and balances are complete and accurate.
Control activities like the treasurer vouching the acquisition of securities by comparing brokers' advices with canceled checks help support the existence and accuracy of recorded transactions but are less directly related to the assertion of completeness. Similarly, comparing current market prices of recorded investments with the brokers' advices on file by the controller assists in the valuation or allocation assertion rather than completeness.