In short, you can use sumaan if you have any form of 'have' before the 'breathed', su'um otherwise. I explain the full system below.
There are two grammatical tense: simple and present perfect.
The simple tense does the duties of English simple present, simple past, or present progressive depending on context, and all verbs are listed in this form in the dictionary.
zu'u bo 'I fly/am flying/flew'
zu'u su'um 'I breathe/am breathing/breathed'
To get the present perfect, add the suffix -aan and collapse the long vowel in the second-to-last syllable, if any. The present perfect form can also act as a past participle.
zu'u boaan 'I have flown'
zu'u sumaan 'I have breathed'
If context isn't enough, you can introduce lexical tense and clarify a simple past with drey 'did' and a simple future with fen 'will': zu'u drey su'um 'I breathed', zu'u fen su'um 'I will breathe'
Here is the lesson on this topic.
Edit: su'um is probably limited to supernatural powers, but the point stands.