A quick look at the meaning of "vorgehen" and why it has the three meanings it has.
vorgehen, der Vorgang, das Vorgehen, hervorgehen aus
The core idea of this root was:
going away, disappearing
This is also commonly considered the origin of to go but other relations are not certain.
The English to go is defective in the sense that it doesn’t have its own past tense form. And it hasn’t had one for more than a thousand years. Instead, it uses the form went, which is taken from the verb to wend. It’s unclear, why to go is defective.
German gehen does have its own past form, but according to German etymologist, the cluster of gehen is actually a combination of two families – one being the one of to go and the other being that of the word of English gang, which ironically was originally about making steps.
Yeah… I know… this was already a bit too nerdy. We’re here to learn German, not do science :)