~게 생각하다
When is it used?
I know about ~라고 생각하다, but I see 생각하다 with 게 for the first time.
+ ~게 여기다; what is this for?

Question

~게 생각하다
When is it used? 
I know about ~라고 생각하다, but I see 생각하다 with 게 for the first time.
+  ~게 여기다; what is this for?

Answer

the 게 in this sense would most likely be the ending of an adverb. So you can say:

행복하게 생각하다 - To think happily
깊게 생각하다 - To think deeply

The same goes for 게 여기다. 여기다 can mean consider, regard...etc. 
심각하게 여기다 - To take something seriously

Hope thank helped!