What does 之 mean in 邓小平之所以推动改革开放...?
所以 means 'because' but it can also be used as a noun for &quot;reason&quot; , as in &quot;不明所以&quot; (don't understand the reason)

邓小平 is a noun,  之=(的),  所以=reason
邓小平(之)所以 = Deng Xiaoping('s) reason (for)


推动改革开放 (promote reform and opening up) is the action that the reason resulted in.

一来是为了提高人民的生活水平，二来是为了让中国经济从计划经济转变到市场经济。 is the description of the reasons


'之所以' is a common phrase for 'the reason why'; 'therefore' because it is so commonly used in literary form.
Example:
&quot;(The reason why) he resigns&quot; = &quot;他(之所以)辭職&quot;
&quot;(The reason why) he ran away&quot; = &quot;他(之所以)逃跑&quot;
The two examples above must be followed by the description of the reason