Questions & Answers about Я пройду через парк и быстро доберусь домой.
Пройду is the future tense of the perfective verb пройти.
- идти = to be going / to go on foot in progress
- пройти = to go through, pass, walk a certain distance, complete the action
So:
- Я иду через парк = I am going through the park
- Я пройду через парк = I will go through the park / I’ll walk through the park
In this sentence, the speaker is talking about a completed future action, so perfective пройду makes sense.
Here, пройду через парк means something like:
- I’ll walk through the park
- I’ll go through the park
- I’ll pass through the park
The prefix про- often adds the idea of passing through or covering a route/distance. So it is not just go, but more specifically go through a place.