You want to offer student-centered active learning, particularly for advanced students.  Speaking tasks certainly represent active learning, as they research and prepare.  But student-centered learning implies giving the students considerable choice in their learning.  

So for example, if the task is a classroom presentation, allow students to choose their topic, and to choose their presentation styles.  

Sure! Students usually find it helpful and less guided when they are left to decide on their own. Presentations can also be ideal providing that there is adequate training on personal, if not social skills, namely exposure, confidence and many abilities, which unfortunately, are rare in our case: Non native Speaker EFL learners.

You need tasks which force them outside their linguistic comfort zone,in different ways. These include: 

1) Tasks for which they lack part of the vocabulary required. This way, they will be forced to use paraphrase and other compensation strategies.

2) Tasks which require descriptive or explanatory precision-.e.g. describing complex processes.

3) Tasks which demand a control of aspects such as register and the use of tactful language. One task I do involves delicate situations in which the students have to say potentially face-threatening things in the most diplomatic , non-confrontational way possible.

Role plays, drama tasks and presentations are some of the activities that could be used to stretch advanced students' language in the ways described above.

Since your students are advanced , I think it is better to develop their fluency by using interaction and communication based activities such as classroom tasks in all its types.  This video may be useful to you .

Liqaa 

https://www.youtube.com/watch?v=Sc4gh5gP1AE

Speaking skill involves more than just pronouncing words , it encompasses different skills such as fluency, motivation....You should define at the early  beginning the skill you want to target by your task .However; in general the following activities provide opportunities for interaction and communication:

Activity1: Class Survey

Activity 2:Conversation Grid

Activity 3: Line Dialogue

Activity 4:Information Gap

Activity5:Language Experience Approach

Activity 6:Games

This ppt presentation may help you

Houda

I do tremendously appreciate your answers as most of them suggest turning the focus on knowledge awareness rather than linguistic competencies.  Thanks Mrs Houda