英辞郎からの引用です。（一部）

熟語10個

in a careful way [manner]
in a cautious manner [way]
in a circumspect way [manner]
in a measured fashion [way, manner]
in a prudent manner [way]
in meticulous fashion [way]
with care ≒carefully
with circumspection
with deliberation（言動などが）
with discretion

副詞12個

carefully
cautiously
circumspectly（実行する前の検討などが）〔【形】circumspect〕
deliberately
discreetly
guardedly
heedfully
meticulously
painstakingly
prudentially
sparingly
studiously