This is the 9770th most frequent French word.
essayant
"Essayant" means "trying" or "attempting."
Here, 'essayant' functions as a present participle of the verb 'essayer', indicating the action occurring at the same time as the main verb 'est tombé'.
Il est tombé en essayant de traverser la rivière.
He fell while trying to cross the river.
In this context, 'essayant' is used to describe an ongoing action that provides a rationale for the following action, 'pose de nombreuses questions'.
Essayant de comprendre, elle a posé de nombreuses questions.
Trying to understand, she asked many questions.
Here, 'essayant' serves to express a concurrent effort during the main action described by 'avancent doucement'.