そこでAccordingly, Now, Therefore, To that end

そこで and したがって are both used at the beginning of a sentence to express one action following another, but differ in nuance and tone. そこで is a general-purpose expression usable in various situations and contexts, like the English 'so' or 'as such'. In contrast, したがって is more formal and has a stricter 'following from that' or 'thus' nuance.

Both describe what follows from a previous situation, but with different nuance. そこで introduces an intentional response to a situation, e.g. 雨が降ってきた。そこで傘をさした ('It started raining, so I opened my umbrella.') すると shows a natural or immediate result, e.g. 雨が降ってきた。すると子供が泣き出した ('It started raining. Then the child started crying.')

Both are typically used at the beginning of a sentence to show what follows from a certain cause or situation. そのため(に) more clearly states the relation and can mean either 'due to that' or 'for that purpose', while そこで is less clear about the relationship between the previous thought and what follows, similar to the English 'as such' or 'in light of that'.

These expressions are similar in that both are used at the beginning of a sentence and can express the outcome of a situation, but they differ in nuance. そこで is relatively vague about the connection between the two events, like the English 'as such' or 'accordingly', while その結果 more specifically conveys that a situation or condition results from the previously mentioned cause.