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The lag effects of utterance to communicative motions in human-robot and in human-CG character greeting interaction have been clarified. In this paper, information presentation timing by an agent based on the time lag effects of utterance to communicative action is analyzed by synthesis for applying to a human-agent interaction support. First, the analysis of a human information presentation action clarifies the average pause and average time delay of utterance. Then, the analysis by synthesis is performed by using an agent of CG character and confirms that the lags of utterance in certain information presentation timing bring communication effects, i.e. the moderate lag is familiar and the longer lag is polite. It is also clarified that it is unnatural to start motions and utterance simultaneously in human-agent interaction. These results demonstrate the importance of timing in human-to-agent embodied interaction and the method to perform an information presentation effectively.