Participial phrase separating main verbs

Let’s say you have the following sentence:

I stood there and wondered what to do next.

Now, let’s say you insert a participial phrase after "there."

I stood there looking at her and wondered what to do next.

Does the verb "wondered" have to become part of the participial phrase (i.e., "wondering what to do next"), or can it remain "wondered"?

I stood there looking at her and wondering what to do next vs. I stood there looking at her and wondered what to do next.