Which of the following actions must a firm take if it fails to maintain net capital of at least 125 percent over a period of time?

If a firm does not maintain a net capital of at least 125 percent, it is required to reduce its business. This requirement is in place to ensure that firms remain financially stable and can meet their obligations to customers and counterparties. By reducing their business, the firm effectively lowers its operational exposure and financial commitments, which can help stabilize their financial position.

Reducing business might involve scaling back on certain operations, cutting expenses, or divesting from certain assets to ensure compliance with regulatory standards. This action is a measure to safeguard the firm's solvency and avoid potential risks associated with operating at a capital level that is deemed insufficient.

While other options such as expanding, increasing capital, or merging might seem viable, they do not directly address the immediate need for compliance with capital requirements. Increasing capital is a more proactive step that can also be taken, but it is not a mandated action like the reduction of business, which is a necessary step to rectify the financial situation and align with regulatory standards.