asks: How do you write a character and their actions when they are much smarter than you?

You don't have to be a genius to write about one. You just have to demonstrate how smart they are in the story. There are different ways to do this.

If your character is book-smart, it will be easy to look up information regarding their areas of expertise. Then during conversation, the character can casually mention that babies have about 100 more bones than adults do, or that polar bears are nearly undetectable by infrared cameras. (Did I look smart just now? I literally went to Google and searched "little known science trivia".) The context of the conversation will matter, of course. The character can't be walking around spouting facts like some kind of Rain Man (unless that's your character). Be thoughtful where these facts will make sense in a conversation. They could be used as a metaphor for something else.

Characters with superior intellects are more challenging to write because their brains just work differently from the average person's. Sherlock Holmes is a great example. He's able to notice things most people don't and then connect that information with other facts. The good news is you don't need to have a Sherlock intellect to write such a character. As the author, you have all the facts already, so all you need to do is divulge some of the more obvious details.

For example, they could be trying to find a missing person, and they're in the house examining photos. One investigator will note that the missing person likes the beach, then the smart one can look more closely and notice a rare plant in the photo, then reveal that the plant could only be found in a certain part of the city. Boom, smart person!

Some people are very smart and they know it. They also let everyone around them know it. Arrogance from feeling superior is a very real thing. Sometimes they project this arrogance as a defense mechanism to hide the fact that they don't actually know much. Or they may project this arrogance because they think that's all their good for. Room for character development!

Still stuck? Think about movie characters that seem very smart to you. Watch how they are portrayed in the movie. Think about some smart friends or coworkers you might have. How do they behave? How do you know they're smart? Think about applying some of those things into your story, and you'll be well on your way.