One example of a four letter synonym for "to go in search of" is "seek." Other examples include "hunt," "fish," "comb" and "root." These words can be used in various ways to replace "to go in search of."
An example of a sentence with the word "seek" is "The conquistador was going to seek the Fountain of Youth." The word "hunt" can be used in a sentence such as "The children spread out across the field to hunt hidden Easter eggs." An example of the word "fish" in a sentence is "The detective took his time sifting through the details to fish an answer from the confusing case."