The word seek is a four letter word that fits the required description of "to go in search of." This is the definition according to Merriam-Webster.
Seek means "to go in search of." According to Merriam-Webster, It is a present-tense verb that can also mean "to make a request for" or "to make an effort to do." Some similar words to seek include cast about, chase, forage, hunt, look up, pursue, quest, search and shop. In sentence structure, one can seek a person, place or thing directly. For example, a common purpose in a court of law is "to seek the truth."