I will assume you know how to connect verbs with the "te-form":
晩【ばん】ご飯【はん】を食【た】べて、寝【ね】る。I will eat dinner and (then) sleep.
So, usually in texts/books, etc. There's a more formal way to do so, which is using the dictionary form instead.
晩【ばん】ご飯【はん】を食【た】べ、寝【ね】る。I will eat dinner, and (then) sleep.
But sometimes, writers do that without using a comma in between verbs/words, and that is what might be throwing you off. So what you have there is 声に出し、行動. We could rewrite it as:
自分を奮い立たせるために、 わざと自分の考えを声に出して、行動を始めた。In order to cheer myself up, I started acting my thoughts out loud.
In your specific case though, I believe we should not use a comma, because it might be using the following pattern 声に出して＋verb/noun that usually means "Doing something out loud".
声に出して読む - To read out loud.