"Fixed the mind" is a phrase that simply denotes a state of concentration or focus. However, there are various ways to express this idea using synonyms. For example, one might say "directed the mind" to convey the notion of purposeful concentration. Alternatively, one could use "concentrated the mind" to emphasize the act of focusing one's attention. "Mentally engaged," "locked in," and "fully absorbed" are also excellent synonyms for the phrase "fixed the mind," as they all connote a deep level of concentration. Ultimately, no matter which synonym is used, the idea of becoming fully engaged with a task or idea remains the same.