Q:

Using Participles in Latin Tenses

In English, we can communicate progressiveness of an action by combining a form of "to be" with a participle.  For instance, "I am acting" is progressive, whereas "I act" is not. 
I am wondering about whether this is possible in Latin.  What if, in Latin, I say "ago" vs. "agens sum".  Is "agens sum" grammatical (or rather, was it grammatical when spoken).  If so, does using the participle in this way communicate progressiveness? 

A:

In my opinion, the answer to your question is no. 
Something like agens sum means "while acting, I am".  In Latin, participles function a bit like subordinate micro-clauses. 

incensus irato, pura mente, ovem agens, sum
  =>
  burning with anger, with a pure mind, leading a sheep, I exist / am. 

To be and a participle does not create a predicate as in English.  The participle is autonomous within the clause. 

A:

In Latin, like in many languages, the usual present tense can be progressive. 
For example, "I am acting" would be simply ago. 
If you want to make a distinction between "I act" and "I am acting", you need to use other words to convey the nature of the action. 
Usually the context alone is enough, but you can add words like "suddenly" or "continuously". 
Latin allows a more similar distinction for past events. 
The imperfect tense is progressive while the perfect tense is not. 
(This may be overly simplified, but does give a good big picture.) 
For example, "I was acting" would be agebam while "I acted" would be egi. 
I agree with Arnaud that agens sum does not mean what you want it to. 
It is grammatical but is not comparable to the English "I am acting". 
The closest interpretation is "I am someone who acts" which comes pretty close to "I am an agent" where the participle has turned into a noun. 
There is rarely need for such constructions, and the Latin present participle behaves mostly like Arnaud explains. 
As LjL commented, modern Romance languages use different constructions for this purpose. 
At least Italian and Spanish use stare + the modern gerund, but this construction is not used in classical Latin. 
Therefore agens sum was unlikely to be the correct choice in vulgar Latin either, so I doubt it has ever had much use in any form of Latin.