Doing something with caution, paying attention to every little detail so you don't mess up.
similar to cautiously.
Watching very carefully.
Watching something carefully
gentle
Carefully analyzing a short piece of writing
Think carefully about (something), typically before making a decision.
to discover how a piece of writer achieves its effects
I think perhaps you mean "peruse." Peruse means to read or examine something carefully.
Carefully look up the word "vague". The definition should help you in your quest.
Noun:a small timepiece typically worn on the wristan act or instance of carefully observing someone or something over a period of timeVerb: to look at or observe carefully, typically over a period of time
Acting suddenly without thinking carefully about what might happen because of what you are doing. (OXFORD Advanced Learner's Dictionary)
Ponder means to think about something carefully and deeply, often with a sense of reflection or contemplation. It involves considering thoughts or ideas thoroughly before coming to a decision or conclusion.