TASK DEFINITION: In this task, you are given two sentences in the English language (Sentence 1 and Sentence 2). Your task is to identify the connecting word between the two sentences.
PROBLEM: Sentence 1:While the amphitheater 's capacity more than doubled , no known event warranted such an effort . Sentence 2:In fact , some evidence suggests that the population of Caesarodonum ( Tours ) had stopped growing by that time .

SOLUTION: in fact

PROBLEM: Sentence 1:Like many universities and colleges in the United States , Stanford does not make use of hoods for bachelors . Sentence 2:Instead , bachelors use a stole bearing the university seal at graduation ceremonies .

SOLUTION: instead

PROBLEM: Sentence 1:When Toothy is drilling , the drill 's battery goes dead , much to his disappointment . Sentence 2:However , after Toothy managed to get another battery .

SOLUTION:
however