[subject] + 渐渐 / 逐渐 + [verb] / [adjective]
渐渐地 + [clause]
渐渐 and 逐渐 mean "gradually". They go before a verb or adjective that describes a change, and the sentence usually ends in 了 or carries a change verb such as 变, 习惯 or 提高.
渐渐 is neutral and common in stories. It can take 地 and stand at the very start of the sentence, before the subject. 逐渐 is more written – reports, news, essays – and goes straight before the verb, after the subject.
A verb or adjective that describes no change has nothing for 渐渐 to describe.
慢慢 also means "slowly" and can describe an action you do on purpose, including in a request. 渐渐 describes change that happens by itself, so it never goes in an instruction.