Learn Spanish (Latin America): A continuación explico el problema.

In Spanish, the present tense is very commonly used to talk about actions that are going to happen in the immediate future, or things you are just about to do. Using explico here sounds more natural and immediate than using the future tense like explicaré.

Is a continuación a discourse connector like the ones in this lesson?

Yes! While this lesson focuses on contrasting ideas, a continuación is a connector used for sequencing. It translates to "next," "below," or "following this." It is a great tool for structuring your thoughts, especially when giving a presentation or writing an essay.

Could I use próximo instead of a continuación to mean "next" here?

Not in this context. Próximo is an adjective used to describe nouns, like dates or events (for example, el próximo año for "next year"). When you want to say "next" to introduce the next step in a sequence or a speech, you should use a connector like a continuación, luego, or después.