Here are some synonyms:
* Rethink
* Reevaluate
* Review
* Reassess
* Reexamine
Here are some examples of how to use "reconsider" in a sentence:
* "I urge you to reconsider your decision to quit your job."
* "The council is reconsidering its plans for the new library."
* "After much thought, I have decided to reconsider my offer."
Essentially, "reconsider" implies a willingness to change your mind based on new information or a different perspective.