"slowly proceeding" is correct and usable in written English
You can use it when describing the action of someone or something moving slowly with purpose, as if they have an ultimate goal in mind. For example, "The boat was slowly proceeding downstream, its destination uncertain."
And reforms of the judicial system, though blocked at the federal level, are slowly proceeding state by state.The AFI apart, corruption and incompetence remain hallmarks of Mexico's police.
Stocks changed little Tuesday even though promising data from the retail sector fed optimism that the economic recovery was slowly proceeding.
The slowly proceeding demographic and economic recovery was reversed as the looting armies and an outbreak of bubonic plague decimated the people.
Before that, though, the set starts rather slowly, proceeding through older songs from their Amassakoul album of 2004 at a nodding pace.
However, the process of sedentarising Tibetan nomads in the Amdo area has already been slowly proceeding for a long time.
These cases included fractures to the ribs with slowly proceeding haematoma, and mild initial brain contusions in combination with breathing difficulties, leading to severe brain oedema.
The roller coaster, still moving slowly, proceeds to a room filled with burial treasure gleaming seductively in the semidarkness.
He stabilized himself and a piece of notebook paper using the heel of his right hand, and then, slowly, proceeded to draw remarkably straight lines.
They faced the audience one last time and slowly proceeded out the theater and down the street, their progress captured by video projections.
The Allied ship returned to Brindisi and the Austrians slowly proceeded back to base.
The amplified wave slowly proceeded west-northwestward along Central America, bringing heavy rainfall to the area.
