Inspect, investigate, examine, analyse, scrutinise...
The root word of "carefully" is "care," which means to be concerned or attentive.
A word that means to read very carefully is peruse.
"recherche" is the French word for "search".
search, research
The word is "diplomatic," which means choosing words carefully to avoid causing offense or misunderstandings.
precise
duly
observe
Gently Gently
Peruse
To overlook or observe closely
The word you are looking for is "contemplate." It means to think deeply or carefully about something.