What is the author's purpose in this passage? –The War of the Worlds,

You should remove the following sentence: "The action slows when Annie and Anagnos have a discussion, and the play becomes boring" from the summary.

The problem with this sentence is that it gives a value judgement ("boring"). This is an opinion, and it is not what is expected from a student when writing a summary. You should stick to the facts and the narration.

Besides, a summary is meant to be giving as much information in as few words as possible, and this sentence is only adding unnecessary length to it.