"proceed to explore" is correct and usable in written English.
You can use it when you want to indicate that you are going to start looking into something. For example: "I am interested in the new technology, so I will proceed to explore its potential uses."
It is curious that so many discussions of management begin with exhortations to clarify objectives, and then, as if the nature of objectives were well known, proceed to explore some other aspect of the matter at hand.
In addition, this review will proceed to explore the possible novel physiological mechanisms, through which exercise may confer any observed changes.
Having discovered through personal experience the reason for this selective advantage, the students proceed to explore an environment that changes over time, starting out white and gradually turning brown as the snow melts (Figure 6).
In order to justify this idea, we proceed to explore and quantify the variety of mechanisms underlying the robustness inherent in each time scale.
By representing proteins folds and functions in form of a graph connected by the prototypes one can proceed to explore the emergence of protein functions as combinations of prototypes.
In case of a suspected PAC, even when such a cyst is actually found, the surgeon should proceed to explore and to thoroughly inspect the ventral portion of the spinal cord and the dural sac.
"And, I proceeded to explore all of life's other facets.
Ms. Oberlin proceeded to explore proclamations of female autonomy in songs that span more than a century and many genres.
Never apologetic about his identity - "I'm the only one doing Scottish Painting" - he proceeded to explore and confront the varied extremes of the national psyche.
The novel opens with a vivid description of what takes place one evening at that checkpoint, and proceeds to explore the ramifications of the incident.
He acknowledged that this might sound "at first like an extreme view" but proceeded to explore all the major themes of social theory in the light of this idea, conducting his survey in a highly readable and entertaining way.
