Here is a slightly artificial sentence that illustrates the use of a participle phrase with a present participle, with an active meaning: Many companies evaluate students, basing their judgment on their teachers' …
Basing here is the present or active participle; it modifies the Agent of the verb base, the one who performs the action, namely us. Now recast the original proposition into the passive voice, as it is …
It would be wrong, then, to have assumed that Jupiter VIII was the eighth moon from Jupiter, basing our assumption on "VIII". We don't even need to know the astronomical fact here …