This would be , not . The latter is used to say something was carried out/executed.
Here, is actually part of the format of . When you add to a -form of a verb, it is as if the verb is currently being acted out.
> In your example, the police were likely to begin a process of following him. To say, the police began to actively follow him. It conveys a sense of progression of some event.
The other used of a directional verb you will see is , which is to say some verb arrived at something, or that something was done, and arrived at that state.
> would be something became fat after some process, to say it arrived at being fat.