A truly adjectival (or 'adjunctive') participle phrase is quite distinctive in that it serves to identify a noun referent in the manner of a restrictive relative clause, as 'playing tennis' in
The boy playing tennis is Peter.
(= The boy who is playing tennis...)
N.B. Adverbial (sometimes termed 'disjunctive') participle phrases are obligatorily set off by commas. I have inserted the missing comma before 'avoiding' in your text.