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を進めている

is proceeding with

→ を
phrase Rare #37,188
is proceeding with Used to describe someone continuing or making progress with an activity, investigation, discussion, or plan. The object marked by を is what is being advanced or pursued.
JA: 会社は新しいプロジェクトを進めている。
EN: The company is proceeding with a new project.

盗人は巧妙に話を進めている

The thief is skillfully steering the conversation.

— 羅生門 (1950)

警察は捜査を進めている。

The police are carrying out their investigation.

我々も色々な観点から検討を進めている。

We are also examining the matter from various perspectives.