The phrase is "take a different tack."
Not "Take a different tact."
In this context, tack refers to (according to Merriam-Webster's) changing "the direction of (a sailing ship) when sailing close-hauled by turning the bow to the wind and shifting the sails so as to fall off on the other side at about the same angle as before."
In other words, to change direction.
Tact mostly means you're sensitive and skillful in dealing with others.