そこで means "so", "so then": given the situation just described, someone does something about it. It opens the second sentence, and that sentence is a deliberate action or decision taken in response.
。、。
The road was jammed. So I decided to take another route.
。、。
The budget wasn't enough. So we changed the plan.
。、。
The children looked bored, so I took them to the park.
そこで or それで
links any cause to any result, including things nobody chose – being late, feeling ill. そこで only introduces what someone decided to do about the situation, so a result that just happened takes それで.
。、。
It started to rain, and that made me late.
。、。
It started to rain, so I bought an umbrella.
- × 雨が降ってきた。そこで、遅刻した → 雨が降ってきた。それで、遅刻した
それで is also the more conversational of the two. そこで fits stories, reports and presentations.
Usage notes
These go beyond そこで as "so".
Leading into a proposal
In a meeting or a presentation, そこで turns from the problem just laid out to what you are proposing or asking.
。
This brings me to a question for all of you.
"There"
そこで can also be plus , "at that place".
。。
There's a café in front of the station. I'll wait there.
Lingaku