Write a paragraph explaining how Odysseus uses his "guile" to avoid "succumbing" to Circe.
It is certainly true that Odysseus is a person of cunning and guile, but his initial encounter with Circe is facilitated by a discussion with one of the cleverest beings in the Greek world, the god Hermes.
Before Odysseus meets Circe, Hermes comes down to Circe's island and tells Odysseus what he will have to do to avoid being transformed into an animal (as had happened to some of Odysseus' men). Hermes also gives Odysseus a special plant that will protect him against Circe's magic.
So, thanks to detailed instructions from Hermes, Odysseus avoids being turned into a pig (or suffering some other strange fate).
As for "succumbing," Hermes actually gives Odysseus permission to succumb, at least sexually, to Circe's "charms." In Odyssey 10, Hermes states:
Then she’ll invite you to her bed, and don’t refuse the goddess’ favours, if you want her to free your men, and care for you too. But make her swear a solemn oath by the blessed gods that she won’t try to harm you with her mischief, lest when you are naked she robs you of courage and manhood.” (A.S. Kline translation)
So, in some ways, Odysseus does succumb to Circe, as he follows Hermes' instructions quite closely. Indeed, Odysseus ends up staying with Circe for an entire year.
In sum, I'm not sure Odysseus uses his guile to avoid succumbing to Circe. In Odyssey 10, any guile used belongs to Hermes in my view.