By recommending policy initiatives to state legislators and coordinating with state agencies that administer programs and implement policies, the governor is demonstrating his or her role as

Chief Legislator

Explanation:

The role of Chief Legislator is something that is mostly associated with that of the President as Section 3 of Article II of the Constitution of the United States gives this power to the President. However, the Governor can also exercise this power at the state or provincial level. The role provides the opportunity to the Governor to formulate policy initiatives. They can also coordinate with the appropriate agencies and the implementing and/or regulating agencies for their input as well. Hence, the given description is of Chief Legislator role and the Governor will demonstrate his or her role as Chief Legislator by doing this.