When we face difficult challenges or complicated problems that need a solution, we must engage our minds and think carefully. That's where the phrase "puts one's thinking cap" comes in, which is a metaphorical expression that means to focus, ponder, meditate, or reflect deeply. Thankfully, there are plenty of synonyms that we can use instead of this phrase. For instance, we can say that we are brainstorming, contemplating, considering, mulling over, ruminating, reflecting, or deliberating. These alternatives all convey the same message of engaging in deep thought, and they are useful when we want to communicate more clearly and vary our vocabulary.