Demonstrate how you would solve issues in team dynamics

Your executive, Mr Bennet, has given you the task of taking over an existing team that cannot move past the Storming stage of group development.

After watching the video you would have seen that there is a conflict of interest regarding a simple activity. Two members of the group are particularly outspoken and abrasive, and their personalities clash, allowing no progress to be made because they are constantly competing for leadership. One shy member of the group refuses to speak up when asked a question and agrees with whatever statement another team member makes. Another pessimistic team member is constantly complaining about time, processes and other team members, but never offers a valuable alternative to issues.

What would you do to improve the team dynamics to create cohesion? What leadership style(s) would you adopt if you were the team leader in this situation?