New Thoughts and Do Goals for Quiet Leader

My whole life I have been told I am quiet or shy. I have been complemented by my managers and peers that I have great ideas but that I need to have a “louder” voice and work at presenting myself better to senior leadership. I am now overly anxious in meetings or speaking and start stumbling on my works. It sounds good in my head but when I try to keep up to the speed of others I struggle. I am an introverted person and enjoy deep talks with people. I am not assertive as I want to be by nature. Being a manager I often lead from behind and don’t have a need to be in the limelight. I do realize in order for me to climb the corporate ladder I need to change and start networking more and be seen as a leader by others. What thoughts can I think to help me? What types of goals or actions could I take/set to get the results and respect I need in my job? Thanks in advance!