To examine something carefully.
search, research
Inspect is to look very carefully at something, checking for deficiencies.
To examine.
The word for "look over carefully" is "scrutinize." It means to examine something in detail and with great care, often to assess its quality or to find any flaws. Scrutinizing typically involves a critical and thorough inspection.
read carefully
Cautiously is another word for carefully.
Strategically
The word that means to look something over at your leisure is "peruse." It suggests taking the time to read or examine something carefully and thoughtfully, often without haste. Perusing can involve a detailed review, allowing for a deeper understanding of the material.
Regard as a verb, or regard as a noun. Please clarify.
Another word for 'hopeful' is 'faith.'
gentle
Cautiously, or watchfully