英文的動名詞疑問，第二個動名詞?

Let us students refer to compound sentence.Here are the new and fuller definitions of the term participle clause in the Compound sentence:-=Main clause + one or more co-ordinate (independent participle) clauses.Hence it is fun to know the participle Compound sentence.
"participle" in grammar is verbal adj quaifying noun but retaining some properties of a verb; eg:- Here is Joe Cool
(a)hanging around---verbal adj----a participial phrase containing a gerund.
(b)(trying to figure out)----verbal adj qualifying noun Joe---a participial adjective clause
(c)+(d) what he is going to do this coming summer------verbal adj including participles going+coming----noun clause to (b)

我應該是這樣:

1. Here is Joe Cool.
2. Joe Cool is hanging around. -> (Joe Cool is) hanging around
3. Joe Cool is trying to figure out one thing. -> (Joe Cool is) trying to figure out (one thing)
4. What is Joe Cool going to do this summer? -> what he is (Joe Cool substituted by "he" and moved before "is") going to do ...

combined into:

=> Here is Joe Cool hanging around trying to figure out what he is going to do this summer.
=> Here is Joe Cool hanging around trying to figure out what to do this summer.
=> Here comes Joe Cool hanging around trying to figure out what to do comes summer.

我猜應該是這樣 (分詞構句)
1. Here is Joe Cool hanging around.
2. Joe Cool is trying to figure out what he is going to do this summer.

=> Here is Joe Cool hanging around ( and Joe Cool is ) trying to figure out what he is going to do this summer.