Common Mistakes / Nuances: ❌ 願う (negau): **願う (negau)** means 'to wish' or 'to hope for'. While you can say '平和を願う' (to wish for peace), it has a more passive nuance than 求める. 願う often implies praying or hoping for something that is largely out of one's control, like a divine intervention or good fortune. 求める, on the other hand, suggests a more proactive, demanding stance. In the sentence, the idea of it being a 'common wish' (共通の願い) that people strive for aligns better with the active pursuit implied by 求める. ❌ 頼む (tanomu): **頼む (tanomu)** means 'to ask a favor' or 'to request' something from a specific person. It is used for concrete actions. For example, you would say 「友達に手伝いを頼む」 (I ask my friend for help). You cannot 'ask a favor of' an abstract concept like 'a peaceful world'. There is no direct recipient of the request, making 頼む grammatically and contextually incorrect here. ❌ 探す (sagasu): **探す (sagasu)** means 'to search for' or 'to look for' something tangible or specific that is lost or needs to be found. For instance, 「鍵を探す」 (to look for one's keys) or 「仕事を探す」 (to look for a job). It is used for finding physical objects, people, or concrete opportunities. It is not used for seeking abstract ideals like peace, making it an unnatural choice in this sentence.

Common Mistakes / Nuances: ❌ 願う (negau): **願う (negau)** means 'to wish' or 'to hope for'. While you can say '平和を願う' (to wish for peace), it has a more passive nuance than 求める. 願う often implies praying or hoping for something that is largely out of one's control, like a divine intervention or good fortune. 求める, on the other hand, suggests a more proactive, demanding stance. In the sentence, the idea of it being a 'common wish' (共通の願い) that people strive for aligns better with the active pursuit implied by 求める. ❌ 頼む (tanomu): **頼む (tanomu)** means 'to ask a favor' or 'to request' something from a specific person. It is used for concrete actions. For example, you would say 「友達に手伝いを頼む」 (I ask my friend for help). You cannot 'ask a favor of' an abstract concept like 'a peaceful world'. There is no direct recipient of the request, making 頼む grammatically and contextually incorrect here. ❌ 探す (sagasu): **探す (sagasu)** means 'to search for' or 'to look for' something tangible or specific that is lost or needs to be found. For instance, 「鍵を探す」 (to look for one's keys) or 「仕事を探す」 (to look for a job). It is used for finding physical objects, people, or concrete opportunities. It is not used for seeking abstract ideals like peace, making it an unnatural choice in this sentence.