I'm trying to find reasonable translations for the following:
Ideally, I'm looking for something short starting with "cogito ergo" but I don't know if that applies in these cases, or if I'm trying to use the wrong English equivalents for what I'm trying to say.
Are there any other synonyms (such as "improve") that could be elegantly translated and make grammatical sense?
What you need are the verb forms "I evolve" and "I progress". Fortunately, many Latin dictionaries list verbs in this particular form. I suggest taking a look at procedo (roughly "to go forward") and melioresco (roughly "to become better"). If they don't look appropriate, please specify what is wrong.
If the meanings of these verbs are close enough to what you want, I suggest
Cogito, ergo procedo. — I think, therefore I progress.
Cogito, ergo melioresco. — I think, therefore I improve.
There is also the verb evolvo, but id doesn't really mean "evolve" in Latin. The origin of the word "progress" is progredior, and that is indeed a possible choice. The English verb comes from the past participle progressus, which also has the form progresso, but it doesn't mean "I progress". The analogy between the different forms is nicer for a non-deponent verb (one ending in -o rather than -or), but that is only a matter of aesthetics.
