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LingakuLingaku[clause]，与此同时，[clause]
[sentence]。与此同时，[sentence]
与此同时 means "at the same time as this": 此 points back at what was just said, and the new clause describes something that happens alongside it. It opens its clause, set off by a comma, and is neutral to written – news reports, essays, presentations.
The two events can be literally simultaneous, or two sides of one development – the second often a cost or a counterweight to the first.
同时 can go inside a clause, after the subject, and join two verbs of the same person: 他同时做两件事 "he does two things at once". 与此同时 refers back to a whole event, so it heads its own clause and can't sit inside one.