Formal alternative for "take on board"

Perhaps digest the information

Understand or assimilate (new information or the significance of something) by a period of reflection.

Similarly, absorb

Take in and assimilate (information, ideas, or experience): she absorbed the information in silence

And, as noted in the prior definition, assimilate

Take in (information, ideas, or culture) and understand fully: Marie tried to assimilate the week’s events

All from Oxford Dictionaries Online